manipulation of light-emitting properties of 2d materials by photonic nanostructures

Manipulation of light-emittingproperties of 2D materials by

photonic nanostructures

A thesis submitted for the degree of

Doctor of Philosophy of

The Australian National University

Haitao Chen

Nonlinear Physics Centre,Research School of Physics and Engineering

December 2017

Declaration

This thesis is an account of research undertaken in the NonlinearPhysics Centre within the Research School of Physics and Engi-neering at the Australian National University between Septem-ber 2014 and September 2017 while I was enrolled for the Doctorof Philosophy degree.

The research has been conducted under the supervision ofProf. Dragomir N. Neshev, Dr. Isabelle Philippa Staude, Dr.Manuel Decker, Dr Alexander S. Solntsev and Prof. Yuri S.Kivshar. However, unless specifically stated otherwise, the ma-terial presented within this thesis is my own original work.

None of the work presented here has ever been submitted forany degree at this or any other institution of learning.

Haitao Chen

December 2017

iii

Publication

Journal Publications

Papers with results included in this thesis

1. Chen, H.; Corboliou, V.; Solntsev, A. S.; Choi, D.-Y.; Vincenti, M. A.; deCeglia, D.; De Angelis, C.; Lu, Y.; Neshev, D. N. "Enhanced second harmonicgeneration from two-dimensional MoSe2 on a silicon waveguide", Light. Sci.Appl. 6, e17060 (2017).

2. Chen, H.; Nanz, S.; Abass, A..; Yan, J.; Gao, T.; Choi, D. Y.; Kivshar,Y. S.; Lu, Y.; Rockstuhl, C.; Neshev, D. N. "Enhanced directional emissionfrom monolayer WSe2 integrated onto a multiresonant silicon-based photonicstructure". ACS Photonics DOI:10.1021/acsphotonics.7b00550 (2017).

3. Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei,J.; Decker, M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D.N. "Manipulation of photoluminescence of two-dimensional MoSe2 by goldnanoantennas". Sci. Rep. 6, 22296 (2016).

4. Chen, H.; Liu, M.; Xu, L.; Neshev, D. N. "Valley-selective directional emis-sion from a monolayer transition metal dichilcogenide mediated by plasmonicnanoantennas". To be submitted to Beilstein Journal of Nanotechnology (In-vited, 2017).

Papers wtih results not included in this thesis

5. Rahmani, M.; Xu, L.; Miroshnichenko, A. E.; Komar, A.; Morales, R. C.;Chen, H., Zarate, Y.; Kruk, S.; Zhang, G.; Neshev, D. N.; Kivshar, Y. S. "Re-versible thermal-tuning of all dielectric metasurfaces". Adv. Funct. Mater.1700580 (2017).

6. Howard, J.; Michael, Chen, H.; Lester, R.; Thorman A.; Chung J. "Spectro-polarimetrc optical systems for imaging plasma internal fields, structures andflows". J. Instrum. 10, 09023 (2015).

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7. Marino G.; Solntsev A. S.; Xu L.; Gili V.; Carletti L.; Poddubny A. N.;Smirnova D.; Chen, H.; Zhang G.; Zayats A.; Angelis C. D.; Leo G.; Kivshar, Y.S.; Sukhorukov A. A.; Neshev, D. N. "Sum-frequency generation and photon-pair creation in AlGaAs nano-resonators". To be submitted.

Selected Conference Presenctations

1. Chen, H.; Nanz, S.; Abass, A..; Yan, J.; Gao, T.; Choi, D. Y.; Kivshar, Y. S.;Lu, Y.; Rockstuhl, C.; Neshev, D. N. "Directional and enhanced photolumi-nescence from multi-resonant WSe2-Si hybrid structure", International Con-ference on Materials for Advanced Technologies (ICMAT), Singapore, June,2017.

2. Chen, H.; Corboliou, V.; Solntsev, A. S.; Choi, D.-Y.; Vincenti, M. A.; deCeglia, D.; De Angelis, C.; Lu, Y.; Neshev, D. N. "Control of second-harmonicgeneration from two-dimensional MoSe2 in a guided wave geometry", Inter-national Conference on Materials for Advanced Technologies (ICMAT), Sin-gapore, June, 2017.

3. Chen, H.; Corboliou, V.; Solntsev, A. S.; Choi, D.-Y.; Vincenti, M. A.; deCeglia, D.; De Angelis, C.; Lu, Y.; Neshev, D. N. "Enhanced second-harmonicgeneration from two-dimensional MoSe2 by waveguide integration", Confer-ence on Lasers and Electro-Optics (CLEO), San Jose, California, United States,May, 2017.

4. Chen, H.; Nanz, S.; Abass, A..; Yan, J.; Gao, T.; Choi, D. Y.; Kivshar, Y.S.; Lu, Y.; Rockstuhl, C.; Neshev, D. N. "Enhanced and directional photolu-minescence from doubly-resonant WSe2-Si hybrid structure ", Conference onLasers and Electro-Optics (CLEO), San Jose, California, United States, May,2017.

5. Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei, J.;Decker, M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D. N. "Ma-nipulation of photoluminescence of 2D MoSe2 by gold nanoantennas", SPIEOptics + Photonics, San Diego, California, United States, August, 2016.

6. Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei, J.;Decker, M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D. N."Tunable photoluminescence of two-dimensional MoSe2 by gold nanoanten-nas", SPIE Photonics Europe, Brussels, Belgium, April, 2016.

7. Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei,J.; Decker, M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D.N. "Control of photoluminescence of two-dimensional MoSe2 by plasmonicnanoantennas", SPIE Micro+Nano Materials, Devices, and Applications, Syd-ney, Australia, December, 2015.

8. Chen, H.; Howard, J.; Michael, Lester, R.; Thorman A.; Chung J. "Syn-chronous coherence imaging of drift waves in MagPIE", 21th Congress of theAustralian Institute of Physics, Canberra, Australia, December, 2014.

Acknowledgments

When I firstly started to write the Acknowledgments part, I followed thesame procedures as I did for other parts: reading the published thesis firstand then trying to following the mature format. However, I felt somethingnot right after writing down "Firstly I would like to thank...", I was runningout of words, I felt these sentences were so "dry" and was far from enough toexpress my appreciation and gratitude, how can a precious more than 3-year-long time be squeezed into one or two pages? Of course, I know that there isnothing wrong to write in this way, it seems I do not even have better way todo it, so I finished the first version following the format listing all the peopleI would like to express my thanks for. However, I still felt somewhere notright.

Until one day, I read an article discussing the difference of expressinggratitude between eastern and western culture. It says, "In Chinese traditions,when you say ’please’ or ’thank you’, you are basically erecting a barrier be-tween you and whomever you are speaking to. For the Chinese, politeness orsuch keqi (standing on ceremony) is associated with formality. As such, whenyou say thank to a friend what you are actually saying to them is that thereis some need for formality between us...". Suddenly, it seems that I found theorigin of my uncomfortable feeling. Having been brought up in a very tra-ditional Chinese family, I still did not fully get used to use thanks naturallyespecially for deep gratitude though I have been in Australian for more than4 years. In the bottom of my heart, I already treat my supervisors, colleagues,friends, families, who are always supportive, as the people I do not need anyformality. I suddenly realized that this is likely the core reason why I feltsomething not right when writing the first version of the Acknowledgments.It is abstract and difficult to discuss the culture influence in detail here, I wantto give out one short story how the people around support my phd.

During the second year of my phd, I spent quite a few months on someproject starting from purchasing equipments and building up the measure-ment setup. We continued with experimental measurements taking lots ofdata. I was so excited when we observed expected phenomena after months’hard work, we took more data and even organized a few discussion sessionswith relevant people awaiting prominent results from this project. However,we found something unusual one day. What’s worse, after careful verificationof the results, it turned out that the observed phenomena was artificial effectfrom one item we borrowed from another department. What a disaster for aphd student. I was so depressed feeling that I could not finish my phd...

Then, Dragomir, the chair of supervisor panel, came immediately after histrip back from Europe and told me "Do not worry, take some break, we arelearning anyway..." with his usual encouraging smile.

ix

One of my lab colleagues, Tingge Gao, helped with verifying the dataagain and again, told me similar story when he was a phd student trying torelease my anxiousness.

My friends organized a trip to the beach after knowing my situation tryingto cheer me up from the depression.

My girlfriend, Ran Gao, who is now my wife, always told me "I trust you,I believe that you could do better ", even though she has little understandingabout my project.

Phd life is meaningful but not always easy, it has ups and downs. WhileI know that I could always count on the support from supervisors, collabora-tors, colleagues, friends and families without the need of any formality, whichmakes my phd life meaningful and colorful. At the end, I want to take thewestern manner saying thanks to all the people that support and accompanyme during my phd, meanwhile, I will hold the deep gratitude in the bottomof my heart as the traditional culture imposes on me.

I would like to acknowledge the Chinese Scholarship Council (CSC), theAustralian Research Council (ARC) Discovery Project (DP) and Center of Ex-cellence Program (CUDOS), for the PhD scholarship and research support.I would further like to thank the ACT node of Australian National Fabri-cation Facility (ANFF) for devices fabrication. The work presented in thisthesis is also partially supported by the Australia-Germany Joint ResearchCo-operation Scheme (DAAD) and the Erasmus Mundus NANOPHI project.

Haitao Chen

at Le Couteur Building,the Australian National University,

September 2017

Abstract

The development of two-dimensional (2D) materials brings up new oppor-tunities for 2D physics and new applications. Among them, semiconductortransition metal dichalcogenides (TMDCs) show quite advanced properties.Especially, in the monolayer limit they become direct-bandgap semiconduc-tors. The monolayer form demonstrates a range of optical effects includingphotoluminescence (PL), valley polarization and second-harmonic generation(SHG), which are important for future optoelectronic applications. However,the light-emitting efficiency of such monolayer TMDCs is generally low due tothe subnanometer light-matter interaction length and defects. To enable theirpractical applications, new schemes are desirable to enhance the emission ef-ficiency and further control properties such as directionality and polarization.

On the other hand, photonic nanostructures show great capability to ma-nipulate light-matter interaction at the nanoscale. Thus, in this thesis, weexplore different schemes to enhance and control emission from monolayerTMDCs by integrating them with resonant photonic nanostructures, includ-ing plasmonic structures, waveguides and nanoantennas. We have success-fully demonstrated integration of monolayer TMDCs into different photonicplatforms experimentally and showed great capability to control the emissionfrom them. Associated theoretical work has also been presented. Our workshows potential important applications for future optoelectronic devices.

In Chapter 1, we firstly introduce the necessary background of the devel-opment of 2D materials and semiconductor optics. Then, we focus on theoptoelectronic properties of 2D TMDCs. The prospect of integration of 2Dmaterials with photonic nanostructures is further discussed.

In Chapter 2, we show integration of a monolayer MoSe2 onto resonantplasmonic nanoantenna. Comprehensive control of the PL emission fromquenching to enhancement is demonstrated by changing the thickness of thespacer between the MoSe2 and nanoantenna. Further simulation results ex-plain the experimental observation well.

In Chapter 3, we demonstrate enhanced and directional PL emission fromWSe2 monolayer integrated onto a silicon photonics structure. This is achievedby coupling the WSe2 into a multi-resonant grating-waveguide structure whichsupports several leaky waveguide modes. Further theoretical work explainsour experimental results well.

In Chapter 4, we propose a plasmonic-TMDCs scheme that could effec-tively separate the PL emission from different valleys of 2D TMDCs into op-posite directions spatially. This is realized by simultaneously exciting bothelectric dipole and quadrupole modes from two-bar plasmonic antenna, theinterference of radiation of these modes induces the spin-locked directionality.

In Chapter 5, we demonstrate enhanced SHG from a monolayer MoSe2.This is achieved by integrating the monolayer onto a waveguide and excitingthe material through evanescent field of the guided modes. The enhancement

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xii

is due to the fact that the waveguide geometry dramatically increases thenonlinear interaction length and allows for phase matching. Theoretical cal-culation further reveals the conversion mechanism in our system and pointsout further directions.

In Chapter 6, we summarize the work and discuss the future prospects inregards to the integration of 2D materials with resonant photonic nanostruc-tures.

Contents

Declaration iii

Publications v

Acknowledgments ix

Abstract xi

1 Introduction 11.1 Thesis statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Overview of two-dimensional (2D) materials . . . . . . . . . . 2

1.2.1 Discovery of 2D materials . . . . . . . . . . . . . . . . . . 21.2.2 Introduction to semiconductor optics . . . . . . . . . . . 4

1.2.2.1 Electron, hole and exciton . . . . . . . . . . . . 41.2.2.2 Direct and indirect bandgap . . . . . . . . . . . 81.2.2.3 Carrier recombination and photoluminescence

(PL) . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.3 2D transition metal dichalcogenides (TMDCs) . . . . . . 9

1.2.3.1 Basic composition and structure . . . . . . . . . 91.2.3.2 Electronic structure . . . . . . . . . . . . . . . . 101.2.3.3 Optical properties and optoelectronic applica-

tions . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Light-emitting properties of 2D TMDCs . . . . . . . . . . . . . . 15

1.3.1 PL properties . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.2 Valley pseudospin . . . . . . . . . . . . . . . . . . . . . . 181.3.3 Nonlinear optical properties of 2D TMDCs . . . . . . . . 201.3.4 Challenges facing 2D TMDCs for photonic applications 22

1.4 Integration of TMDCs with photonic nanostructures . . . . . . 231.4.1 Purcell effect and emission enhancement . . . . . . . . . 231.4.2 Control of light emission from TMDCs through pho-

tonic integration . . . . . . . . . . . . . . . . . . . . . . . 251.5 Motivation and thesis outline . . . . . . . . . . . . . . . . . . . . 26

2 Manipulation of PL from 2D MoSe2 by plasmonic nanoantenna 292.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2 Plasmonic nanoantenna design and sample fabrication . . . . . 322.3 PL characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4 Numerical modeling . . . . . . . . . . . . . . . . . . . . . . . . . 392.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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xiv Contents

3 Enhanced and directional emission from multi-resonant WSe2-Si hy-brid structure 473.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Grating-waveguide fabrication and characterization . . . . . . . 493.3 PL and momentum space characterization . . . . . . . . . . . . 533.4 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . 573.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Valley-based directional emission from monolayer WSe2 mediatedby nanoantenna 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2 Antenna design principles . . . . . . . . . . . . . . . . . . . . . . 664.3 Numerical calculation of two-bar antenna . . . . . . . . . . . . . 684.4 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . 72

5 Enhanced Second-harmonic Generation (SHG) from 2D WSe2 in guided-wave geometry 755.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.2 Waveguide design and sample fabrication . . . . . . . . . . . . . 775.3 SHG characterization . . . . . . . . . . . . . . . . . . . . . . . . . 795.4 Theoretical calculation . . . . . . . . . . . . . . . . . . . . . . . . 835.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6 Conclusion and outlook 896.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A Appendix 93A.1 Fabrication procedures for a-Si grating . . . . . . . . . . . . . . 93A.2 Transmittance characterization setup . . . . . . . . . . . . . . . . 94A.3 PL mapping setup . . . . . . . . . . . . . . . . . . . . . . . . . . 95

References 97

Chapter 1

Introduction

1.1 Thesis statement

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have manyextraordinary electronic, mechanical, optical and chemical properties, andshow great potential to be used in a wide range of applications. In particu-lar, the monolayer form of 2D TMDCs crosses over to become direct-bandgapsemiconductor and shows strong excitonic effects when interacting with light.This opens the door to many optoelectronic applications including atomic-scale single-photon emitter, transistors, novel light-emitting diodes and so on.However, the light emission efficiency of monolayer TMDCs is much lowerthan expected for direct-bandgap semiconductors, which is mainly due tothe fact that the light-matter interaction length is limited by the subnanome-ter thickness, thus prohibiting them from many practical applications. Novelmethods of enhancing the light-emitting efficiency and improving other emis-sion properties are required.

Photonic nanostructures such as plasmonic structures, waveguides andnanoantennas are capable of controlling light-matter interaction at nanoscaleand show great flexibility. Thus, the integration of a monolayer TMDCs withphotonic nanostructures is promising to tune the light-emitting properties ofthese 2D materials. Such integration schemes have shown the capability ofcontrolling the emission from a monolayer TMDCs, for example, ultralowthreshold lasing from monolayer MoS2 has been demonstrated by coupling tophotonic crystal cavity. However, there is far more to explore in this directionin order to further enhance and control light emission from 2D TMDCs.

This thesis aims to develop novel photonic platform to enhance the lightemission from monolayer TMDCs, and further control the other emissionproperties such as polarization and directionality. In general, photonic struc-tures could be categorized into metallic and dielectric structures. They bothhave their own advantages. We explore both regimes of integration of TMDCswith metallic and dielectric structures based on request for linear and nonlin-ear applications.

1

2 Introduction

Following this logic, a brief introduction to discovery of 2D material andsome fundamentals of semiconductor optics are given at the beginning ofSection 1.2, then we move to overview of properties of 2D TMDCs. In Sec-tion 1.3, we focus on discussing the light-emitting properties of 2D TMDCsincluding photoluminescence (PL), single-photon emission, valley polariza-tion and second-harmonic generation (SHG). At the end of this part, we alsodiscuss the challenges facing 2D TMDCs for photonic applications. Followingthis, Section 1.4 firstly introduce the theoretical frame of enhancing sponta-neous emission rate by Purcell effect, and then show the bright prosperity ofintegration of 2D TMDCs with photonic nanostructures, which also justifiesour choice of the thesis topic. Section 1.5 presents motivation and outline ofthe thesis.

1.2 Overview of two-dimensional (2D) materials

’What could we do with layered structures with just the right layers?’ RichardFeynman raised up this question in his famous lecture, ’There’s plenty of roomat the bottom’, in 1959. Among these ’right’ layers, strict 2D materials at atomicscale are particularly interesting and have attracted lots of attention. Seekingfor the real 2D materials in practice had been a long haunting dream.

1.2.1 Discovery of 2D materials

Although having been studied for long time as a theoretical model [1–6], 2Dcrystal of atomic thickness such as graphene was predicted to not exist, asthey were thought thermodynamically unstable [7, 8] and was described aspure ’academic’ material. However, people’s minds changed in 2004 whenfree-standing graphene was unexpectedly found in the lab [9], and particu-larly when the following experiments [10, 11] showed that the charge carriersinside graphene were indeed massless Dirac fermions. Figures 1.1(a) and (b)show the crystal structure of graphene and the first atomic force microscope(AFM) image of the graphene sample, respectively. The discovery of graphenenot only brought Andre Geim and Konstantin Novoselov the 2010 Nobel prizein physics, it also opened the door to a gorgeous world of 2D materials.

When thinned down to a atomic layer, graphene shows quite different anddistinguished characteristics compared to graphite, it even got a nickname of’miracle material’ due to its superior properties. From the perspective view offundamental physics, the charge carriers inside graphene could be describedas massless Dirac fermions, namely, the conduction electrons at low energiesin graphene have a light-like linear dispersion and behave like massless. Theelectronic spectrum of graphene is shown in Fig. 1.1(c), which provides sci-entists with abundance of new physics [20, 21]. In terms of applied science,

§1.2 Overview of two-dimensional (2D) materials 3

Figure 1.1: Superior properties of graphene (a) The crystal structure of graphene: car-bon atoms arranged in a honeycomb lattice [12]. (b) AFM image of the first ex-foliated single-layer graphene showing its atomic thickness [9]; (c) Electronic spec-trum of graphene inferred from experimental results in agreement with theory.This is the spectrum of a zero-gap 2D semiconductor that describes massless Diracfermions with 1/300 the speed of light [13]. (d) Transmittance spectrum of single-layer graphene (open circles) compared with theoretic prediction for two-dimensionalDirac fermions (red and green). The inset shows the transmittance of white light asa function of the number of graphene layers (squares). The dashed lines correspondto an intensity reduction by πα with each added layer [14]. (e) Measured histogramof elastic stiffness from graphene showing high strength [15]. (f) Observed shift in Gpeak spectral position of Raman spectrum from graphene as a function of the changein total dissipated power, indicating superior thermal conductivity [16]. (g) Measuredresponse of longitudinal conductivity to back-gated voltage from graphene encapsu-lated in hexagonal boron-nitride (solid lines) at different temperature, the dashedlines are theoretical calculation, where we could infer the high carrier mobility fromgraphene [17]. (h) Demonstration of extremely high current density sustained bygraphene [18]. (i) Scatter plot of the gas leak rates dependence on the thicknessof graphene layers measured from a graphene-sealed microchamber, indicating thatatomic-scale graphene membrane is impermeable to standard gases including he-lium [19].

4 Introduction

the amazing characteristics graphene owns rise up new opportunities for awide range of applications. These includes but not are not limited to opticalabsorption of exactly πα = 2.3% (α is the fine structure constant) [Fig. 1.1(d)],super-high intrinsic strength [Fig. 1.1(e)], ultrahigh thermal conductivity[Fig. 1.1(f)], amazing room-temperature electron mobility [Fig. 1.1(g)], capa-bility to sustain extremely high densities of electric current [Fig. 1.1(h)] andcomplete impermeability to any gases [Fig. 1.1(i)]. Graphene has shown itspotential to be used in various areas, such as flexible electronics, photonics,energy generation and storage, sensors and metrology, bioapplications, paintsand coating and so on [20–22]. It is almost impossible to name out all the po-tential applications and new physical phenomena graphene has brought to us.This atomically thin material has been an obsession for researchers around theworld since its birth in the lab and new things are still coming out every day.

On the other hand, the message we could take from graphene is that the2D materials have extraordinary properties compared to their bulk forms andhold huge potential for lots of applications, which is not fully explored at all.This inspired people to start looking for other graphene-like materials, such asboron nitride, transition metal dichalcogenides (TMDCs), black phorsphore,silicene and germanene. In particular, TMDCs are semiconductors and haveshown many superior properties for applications in photonics. In this thesis,we will focus on TMDCs. To better serve for our topics, we start reviewingsome basic concepts in semiconductor optics in the following section.

1.2.2 Introduction to semiconductor optics

The core of electronic technology is to control the flow of electrons, and pho-tonics is the technology to control the flow of photons. Semiconductor opto-electronics connect these two technologies: photons create mobile charge car-riers, and charge carriers in turn control the flow of photons. Semiconductor-based optoelectronic devices such as laser, light-emitting diodes have changedour life a lot and this field is still moving on quickly. Thus, studying opticalproperties of semiconductors, which is in the domain of semiconductor op-tics, is essential for fabricating advanced optoelectronic devices.

1.2.2.1 Electron, hole and exciton

Semiconductor is a crystalline or amorphous solid with electrical conductiv-ity between conductor and insulator, typical examples include Si and GaAs.The conductivity of semiconductors could be altered by changing the tem-perature, doping with carriers or illumination with light. Atoms consistingof solid-state semiconductor could not be treated as single entity like hydro-gen atoms, because they interact strongly with other nearby atoms. Thus,the conduction electrons in semiconductor are not bound to single atom, they


collectively belong to all atoms as a whole. In addition, atoms in lattice struc-ture apply periodic potential on the electrons, the solutions to the Schrodingerequations for the electron energy form energy bands. In each band, a greatdeal of discrete energy levels are densely packed together, which could bewell approximated as continuum. The concept of energy bands is illustratedin Fig. 1.2, the conduction and valence band are separated by a bandgap en-ergy Eg. The bandgap energy is an important parameter when describingthe electronic and optical properties of materials, and the value depends onmaterial. For example, the Eg is 1.2 and 1.42 eV (electron volts) for Si andGaAs at room temperature, respectively. The origin of the bandgap could beelucidated by Kronig-Penney model [23].

Figure 1.2: Energy bands in semiconductor. Illustration of energy bands and chargecarriers in semiconductors [23].

.

The electrons in the semiconductor obey the Pauli exclusion principle, thisprinciple says that two or more electrons could not occupy the same quantumstate and electrons fill up the lowest available energy level first. At absolutezero temperature, the valence band is fully occupied while the conductionband is empty, thus material is not conductive at all. However, with increas-ing temperature, some electrons will be thermally excited to transit from va-lence band onto conduction band leaving behind some unoccupied quantumstates called holes. The electrons in the conduction bands act as mobile car-riers and the unoccupied states in valence band allow other electrons to ex-change places with applied electric field. Thus, the holes left in the valenceband could be regarded as carriers with positive charge. The overall effect isthat every electron excitation creates mobile carriers in both conduction andvalence bands, free electron and hole, respectively. The concept of electrontransition is illustrated in Fig. 1.2. The conductivity of semiconductor materi-als increases sharply with temperature as more and more charge carriers aregenerated.

Under certain excitation condition such as light illumination, exciton mightbe formed. Exciton is a bound electron-hole pair, the electron and hole in-teract with each other through Coulomb forces, similar to hydrogen atoms.

6 Introduction

There are two basic types of excitons, free excitons and tightly bound exci-tons. The free excitons have large radius and are delocalized states, thus theycan move freely throughout crystal. In contrast, tightly bound excitons havesmall radius and are bound to specific atom or molecule. Excitons can onlyexist in stable form when their attractive potential is large enough to pro-tect them from collisions with phonons, the energy of these bound statesis called binding energy. Excitons play an important role in determiningthe electronic and optical properties of semiconductors, especially for low-dimensional ones [24]. Other hybrid particle such as trion (bound statesof two electrons and one hole, or one electron and two holes) or biexciton(bound states of two exciton) might be formed as well in some semiconductorsystems.

Fermi level

At temperature T under thermal equilibrium, the law of statistical mechanicssays that the probability of a quantum state with energy E is occupied, isgiven by the Fermi function

f (E) =1

exp[(E− E f )/KT] + 1(1.1)

where K is Boltzmann’s constant, and E f is a constant called Fermi energyor Fermi level. As can be observed from Eq. 1.1, f (E f ) = 1

2 , which meansthat the probability for electrons to take quantum states with energy of E f is12 . The Fermi level is an important parameter when describing the electronicstructure of semiconductor.

Effective mass

Energy-momentum relation (E− k) plays an essential role in accordance withwave mechanics. In free space, the energy E and momentum p relation forelectron with mass m0 (9.1× 10−31 kg) could be obtained by solving the onedimensional time-independent Schrodinger equation, the solution is shownin Eq. 1.2. We could see from the equation that the E− k relation is simply ina form of parabola.

E =p2

2m0=

h2k2

2m0(1.2)

where h is the planck constant, p is the magnitude of the momentum, k is themagnitude of the wavevector k=p/h.

In semiconductor, the motion of electrons is also governed by the Schrodinger


Figure 1.3: Energy-momentum relation for Si and GaAs. Cross section of the energy-momentum relation for conduction (Ec) and valence (Ev) band for Si and GaAs alongtwo crytal directions, [111] represents the right diection and [100] the left direc-tion. [23]

.

equation, but with a periodic potential created by charges in the crystal latticestructure as discussed. This effect results in not only separated energy bands,but also different Energy-momentum relations. The E− k relations for bothconduction and valence bands in Si and GaAs are shown in Fig.1.3. In addi-tion, since the crystal structure is not always isotropic, the energy of electronsdepends on both the magnitude and direction of the momentum. Fig.1.3 onlyshows the E− k diagram for two specific directions.

Though the energy-momentum relation for electrons is quite different fromfree ones, while we could still observe from Fig.1.3 that the E − k relationcould be approximated by parabola at the bottom of the conduction band.The approximated relation is in the form

E = Ec +h2k2

2mc(1.3)

where Ec is the minimum energy in the conduction band and k is measuredfrom the lowest point.

Compared Eq. 1.4 and Eq. 1.2, we could see that the behavior of electronsin the conduction band and the free electron is similar, but with a differentmass (mc). The mc is known as electron (conduction-band) effective mass.Thus, the effects that the lattices of ions apply on the motion of electron areincorporated into the effective mass, which is also the physical meaning ofthis quantity.

In the same manner, the E− k diagram near the top of the valence bandcould be approximated as

E = Ev −h2k2

2mv. (1.4)

8 Introduction

where Ev = Ec − Eg represents the maximum energy in the valence band, mvis the effective mass of hole (valence band). Similarly, the mv accounts for theinfluence of the ion lattice on the valence-band holes.

The effective mass depends on both the crystal structure of material andthe momentum direction, because the inter-atomic interaction in a crystal isorientation dependent. In addition, the effective mass varies with the bandtaken into consideration. Actually, there are usually a few parabolas coexist-ing at the top of the valence band depending on the types of holes.

Spin-orbit coupling

In an atom, electron’s spin interacts with the magnetic field generated by itsorbital movement around the nucleus, which is a typical example of spin-orbit coupling or interaction. This spin-orbit interaction results in shifting ofthe electron’s energy levels, the detectable signatures are the splitting of thespectral lines from atoms. Similarly, in solid semiconductor, electron’s spinmomentum interacts with its orbital angular momentum, which results in asplitting of the energy bands. In solids, the spin-orbit coupling also relates tothe dimension and symmetry of the materials [25]. In 2D materials, spin-orbitcoupling plays a significant role [26].

1.2.2.2 Direct and indirect bandgap

Based on the band structure, semiconductor materials could be categorizedinto two groups: direct- and indirect-bandgap materials. Direct-bandgap ma-terials refer to semiconductors that have the same wavenumber k (momen-tum) for the conduction-band minimum and the valence-band maximum en-ergy. Materials that do not satisfy this condition are indirect bandgap. Asobserved from Fig. 1.3, GaAs has indirect bandgap while Si does not. Own-ing a direct bandgap or not makes a significant difference for semiconductors,especially when used as emitters. This is because electron transition from theconduction to valence band in indirect-bandgap materials must involve sub-stantial momentum change of electrons, which requires much more effortscompared to direct-bandgap ones. For example, GaAs is good light emitter,while Si is not.

1.2.2.3 Carrier recombination and photoluminescence (PL)

PL is the light emitted by a system following the absorption of photons. In asemiconductor, different mechanisms could lead to absorption and emissionof light. The main ones are listed below.


• Interband transition. An absorbed photon could enable electrons to tran-sit from the valence band to conduction band, creating an electron-holepair. The combination of electrons and holes will be accommodated withphoton emission.• Impurity-to-band transition. This process usually happens in doped ma-

terials. Absorption of photon could enable transition between a dopantand bands. The recombination process might be accompanied with ra-diative photon emission.• Excitonic transition. The absorption of photon could enable the forma-

tion of exciton. The recombination of the electron and hole might resultin photon emission, called exciton annihilation. Recombination of hy-brid particles such as trion and biexciton might be involved in radiativeemission too.

The above processes might also involve nonradiative processes, for exam-ple, interband transition might be assisted by one or a few phonons. Thereare also other nonradiative processes such as intra-band transition (transitioninside bands) and phonon transition. The internal quantum efficiency ηi forphoton emission of a semiconductor material is defined as the ratio betweenthe radiative electron-hole recombination rate and total recombination rate.The internal quantum efficiency is an important parameter to describe thelight emission efficiency of a material. Usually, it is expressed in the form

ηi =rr

r=

rr

rr + rnr. (1.5)

where r = rr + rnr is the total recombination rate, rr and rnr are the radiativeand nonradiative recombination rate, respectively.

So far, we have introduced some fundamental concepts in semiconductoroptics including bandgap, exciton, internal quantum efficiency and so on. Inthe following section, we will focus on discussing the optical and electronicproperties of 2D TMDCs, where these concepts will appear often.

1.2.3 2D transition metal dichalcogenides (TMDCs)

1.2.3.1 Basic composition and structure

TMDCs refer to a group of materials with the formula MX2, where M is atransition metal element from group IV (Zr, Ti, Hf and so on), group V (suchas V, Nb or Ta) or group VI (Mo, W and so on) in the periodic table, and X isa chalcogen (S, Se or Te). These materials possess many interesting electronic,mechanical, optical, chemical and thermal properties and have been studiedby researchers for a long time [27–29]. Figure 1.4(a) shows a picture of thebulk form of MoS2, one example of TMDCs, which has been used as dry

10 Introduction

lubricant and catalysis. Generally, these materials have layered structures ofthe form X–M–X, a plane of metal atoms sandwiched by the chalcogen atomsin two hexagonal planes, as shown in Fig. 1.4(b). Adjacent layers are heldtogether weakly by van-der-Waals forces to form the bulk crystal in variouspolytypes, which are different in stacking orders and metal atom coordina-tion, as shown in Fig. 1.4(c). The overall symmetry of TMDCs is hexagonalor rhombohedral, and the metal atoms have octahedral or trigonal prismaticcoordination [30].

Inspired by graphene, the monolayer of TMDCs could also be formed bymicromechanical cleavage from bulk crystal, Figure 1.4(d) shows the first re-ported microscopic image of the monolayer MoS2 prepared by cleavage. Fig-ure 1.4(e) shows the atomic force microscopic image of the sample shown inFig. 1.4(d). Figure 1.4(f) shows the cross-sectional plot along the red line inFig. 1.4(e), which shows that the monolayer thickness of TMDCs is around0.65 nm. Despite that the bulk form of TMDCs has been studied for a longtime, the same material shows quite distinguished and advanced propertieswhen thinned down to atomically thick layer, especially in a monolayer form.In particular, semiconducting TMDCs (MoS2, MoSe2, WS2, WSe2 and so on)show great potential for photonic applications. In the further section, we willdiscuss in more details the properties of 2D TMDCs.

1.2.3.2 Electronic structure

The 2D versions of TMDCs offer properties that are complementary to yetdistinct from those in graphene. Graphene by nature is semi-metallic with-out a bandgap and only trivial bandgap (<0.25 eV) could be obtained fromengineering [34], which does not fit with digital electronics and greatly limitsits applications where semiconductors are needed. In contrast, 2D TMDCssuch as MoS2, MoSe2, WS2, WSe2 are semiconductors and have bandgapsof amplitudes comparable to conventional group III–V ones [35, 36]. Espe-cially, in the monolayer form, TMDCs such as MoS2 cross over to becomedirect bandgap (indirect bandgap in bulk) with gaps located at the K andK’ points [35, 37] of the electronic spectrum. This is a result of an increasedindirect-gap size due to the substantial quantum confinement effect in theout-of-plane direction, while the direct gaps at the K and K’ points remain al-most unaffected [7,38,39]. Figure 1.4(g) shows the band structure of bulk andmonolayer MoS2 calculated from first-principles density functional theory(DFT) [33]. In particular, 2D material are promising to scale the transistors indigital electronics to ever-smaller dimensions considering their atomic thick-ness and the lack of short-channel effects [40]. Semiconductor 2D TMDCs aresuitable as channel materials in field-effect transistors, as they are structurallystable and have carrier mobilities comparable to Si [41,42]. Figure 1.4(h) showsthe schematic image of the first top-gated transistor based on a monolayerMoS2, which showed excellent on/off current ratio (~108), room tempera-ture mobility of over 200 cm2 V−1 S−1 and subthreshold swing of 74 mW per


Figure 1.4: Basic properties of 2D TMDCs. (a) Image of bulk MoS2 about 1cm long [30].(b) Schematic of the three-dimensional image of a typical MX2 structure, in whichthe yellow atoms represents for chalcogen (X) and the grey ones as metal atoms(M) [31]. (c) Schematic representation of MX2 polytypes of different structures: 2H(hexagonal symmetry), 3R (rhombohedral symmetry) and 1T (tetragonal symmetry).The yellow atoms are chalcogen (X) and the grey atoms are the metal (M). The latticeconstants are in the range of 3.1 to 3.7 Å depending on materials [32]. (d) Opticalimage of the first single-layer MoS2 obtained by micromechanical cleavage [31]. (e,f)Atomic force microscopic image of a single layer of MoS2 on a SiO2/Si substrate(e),and the cross-sectional plot along the red line (f) [31]. (g) Band structures of bulkand monolayer MoS2 calculated from first-principles density functional theory. Thehorizontal dashed line represents the Fermi level [33]. (h) Schematic structures of thefirst transistor built based on a monolayer MoS2 [31].

.

12 Introduction

decade [31]. In contrast, graphene-based transistors could not achieve highon/off ratio due to the lack of bandgap.

The electronic structure of monolayer TMDCs can be modeled through aneffective 2D massive Dirac Hamiltonian with the spin and valley pseudospin(K or K’) degree of freedom, where valley pseudospin refers to degenerateenergy extrema in momentum space [26, 43]. As shown in Fig. 1.4(b), themonolayer TMDCs has out-of-plane mirror symmetry, while no in-plane in-version symmetry [26]. Besides, spin-orbit coupling is strong in 2D TMDCsarising from the d orbitals of the heavy metal atoms [44]. The strong spin-orbit coupling, together with the inversion symmetry breaking, bring lots ofvalley-contrasting optical [26,45–49] and electronic [26,50,51] properties in 2DTMDCs, thus a wide range of related applications. The valley-selective lightemission from 2D TMDCs will be discussed later. In addition, the electricaltransport properties in monolayer TMDCs are also valley-dependent [50], forexample, the valley Hall Effect (in analogy to the spin Hall Effect) has beendemonstrated in monolayer MoS2 [52].

Table 1.1: Electronic properties of selected 2D TMDCs [36].

MoS2 MoSe2 WS2 WSe2

Effective masses (in m0) [26] ~0.5 ~0.6 ~0.4 ~0.4

Optical gap Eg(eV) ~2 [35, 37, 53] ~1.7 [54] ~2.1 [55] ~1.75 [49, 56–58]

Exciton binding energy (eV) ~0.55 [59] or0.9 [60] (Th.)~0.2 or 0.4 [61](Exp.)

~0.5 [59] (Th.)~0.6 [62](Exp.)

~0.5 [59](Th.)~0.4[56] or 0.7 [55](Exp.)

~0.45 [59] (Th.)0.4 [57](Exp.)

Conduction band spin–orbitsplitting (meV) [63]

–3 –20 30 35

Valence band spin–orbitsplitting (meV) [26, 63]

~150 ~180 ~430 ~470

Th. and Exp. represent theoretical and experimental results, respectively. m0 is the electron mass.

Besides, 2D TMDCs have multiple polymorphs in crystalline structures,including 1H or 1T for monolayer and 1T, 2H and 3R for a few layers, asindicated in Fig. 1.4(c). This variation in their structure and composition en-ables broad tunability in functionalities. Table 1.1 [36] lists the basic electronicproperties of the group-VI TMDCs, where we see that the variation in com-position provides characteristics in a broad range, while graphene does nothave flexibility in this respect.

1.2.3.3 Optical properties and optoelectronic applications

The electronic structure of 2D TMDCs discussed above directly influencestheir optical properties. Compared to conventional semiconductor materials,the exciton binding energy of a monolayer TMDCs is around one order of


magnitude larger, as predicted by theory [59, 60, 64–66] and verified by ex-periments [55–58]. The large exciton binding energy induces strong excitoniceffects in these materials. For example, the optical absorption spectrum showssharp resonant features [35, 37], which is consequence of the dominating di-rect transitions between the valance and conduction band states around theK and K’ points [26, 43]. The strong excitonic effects cause a significant trans-fer of oscillator strengths from the band-to-band transition to the 1s excitonstate [67]. The ratio of the oscillator strength of the 1s to the band-to-bandtransitions is up to 100 [36, 68, 69]. This large exciton oscillator strength in-duces strong light-matter interaction for these 2D TMDCs. Absorbance ashigh as 0.1-0.3 have been reported for a monolayer of MoS2 [35, 53]. Besides,the strong excitonic effects also lead to short 1s radiative lifetime, which isinversely proportional to the oscillator strength [68, 69].

Furthermore, higher-order excitonic quasiparticles such as trion [53, 54]and bi-exciton [70, 71] have also been observed in 2D TMDCs. Interestingly,these quasiparticles also have much larger (roughly an order) binding en-ergy than those in conventional quasi-2D semiconductors [53,54,70–72], whichmakes them observable even at room temperature. These might bring manypossible applications such as creation of high-temperature and high-densitycoherent quantum states of excitons [73].

In addition, excitons trapped at anisotropic potentials from spatially local-ized defects in 2D TMDCs give rise to single-photon emission [74–77], whichis indispensable for quantum optics and photonic quantum technologies [78].More details will be given in Sec. 1.3.1.

Consequently, the exceptional electronic and optical properties of 2D TMDCsgive rise to exciting new physics, as well as opening the door to many noveloptoelectronic applications. 2D TMDCs-based photodetectors working via themechanism of photoconduction [35, 52, 79, 83, 85, 86] and photocurrent [80, 81,87–92], structure of in-plane [80, 87–89, 91, 92] and out-of-plane junctions [81,83,90,93], have all been demonstrated experimentally. These 2D TMDCs pho-todetectors mostly operate on the basis of photovoltaic effect and have lowerdark current, compared to graphene-based ones. Responsivity as high as 880A W−1 has been reported [79]. A schematic photograph of one of such de-vices is shown in Fig. 1.5(a). Energy-harvesting device based on a monolayerof WSe2 with power conversion efficiency comparable to a conventional bulkone has also been demonstrated [80]. The relation between the photocurrentand the bias voltage under different conditions are shown in Fig. 1.5(b). Whatis more, heterostructure consisting of different kinds of 2D TMDCs with gate-tunable photovoltaic response have shown great potential for optoelectronicapplications. One example of the device structures is shown in Fig. 1.5(c) [81].In addition, devices based on graphene-TMDCs junctions also offer great op-portunities for various optoelectronic applications [82, 83, 94, 95]. Photore-sponse down to a few ps has been demonstrated from a monolayer graphene/WSe2/graphene device [82], as shown in Fig. 1.5(d). External quantum

14 Introduction

Figure 1.5: 2D TMDCs-based photodetectors and modulators. (a) Schematic of a mono-layer MoS2-based photoconductor showing high sensitivity. The top image showsthe photocurrent mapping of the device, where we could observe a hotspot at thelocation of the monolayer MoS2 [79]. (b) Photocurrent dependence on the bias volt-age for a monolayer WSe2 device with split gate electrodes (top inset) under variousbias conditions. Solid green/blue lines, p-n/n-p; dashed green/blue lines, n-n/p-p.The electrical power Pel from the device could be extracted when working as a diode.The low inset shows the relation between Pel and the bias voltage [80]. (c) Schematicrepresentation of a MoS2/WSe2 heterojunction device with lateral metal contacts,showing gate-tunable photovoltaic response. The top inset shows the enlarged crys-tal structure [81]. (d) Time-resolved photocurrent from graphene/WSe2/grapheneheterostructure photodetector for different thickness of WSe2. The response time formonolayer device extracted here is around 5.5 ps [82]. (e) Photocurrent as a functionof the bias voltage for a graphene/WSe2/graphene device under laser illuminationenergy of 2.54 eV [83]. (f) Image of a TMDC-based saturable absorber modulatedvisible fiber laser [84].

.

§1.3 Light-emitting properties of 2D TMDCs 15

efficiency as high as 50% has been observed from TMDC-graphene struc-tures [83, 94]. Figure 1.5(e) shows the photocurrent dependence on the biasvoltage for one of the examples. Besides, TMDCs-based saturable absorbermodulated fiber laser in visible range has been demonstrated too [84,96], oneexample is shown in Fig. 1.5(f). Considering the rich variation of the 2D ma-terials, there is great potential to explore TMDCs-based heterostructures forapplications.

In particular, the 2D confinement, strong excitonic effects, spin-valley cou-pling and inversion-symmetry breaking in 2D TMDCs give rise to many inter-esting light-emitting properties, such as PL, single-photon emission, SHG andso on. These light-emitting properties make 2D TMDCs potentially serve asversatile light sources, which is missing in graphene. In the following section,we will focus on discussing various light-emitting properties in 2D TMDCs.

1.3 Light-emitting properties of 2D TMDCs

1.3.1 PL properties

As discussed above, the monolayer TMDCs cross over to become direct bandgapsemiconductors and show strong excitonic PL emission at the atomic level [35,37]. Figure 1.6(a) shows the PL spectra from a monolayer and a bilayerMoS2 at room temperature, where we could observe that the single layerexhibits PL orders of magnitude stronger than that of the bilayer. On theother hand, the wide range of bandgaps of the 2D TMDCs, as shown in Ta-ble 1.1, offer vast options of PL emission in the visible and near-infrared range.What’s more, the PL spectral position and intensity from 2D TMDCs couldbe tuned by strain [97][Fig. 1.6(b)], electrical gating [54][Fig. 1.6(c)], chemicaldoping [98][Fig. 1.6(d)], temperature [99][Fig. 1.6(e)], composition [100][Fig. 1.6(f)]and so on. In addition, the heterostructure consisting of different 2D TMDCsadd more options for tunable PL emission [81, 101, 102]. The vast varietyand broad tunability make 2D TMDCs ideal candidates for the light-emittinglayers for flexible optoelectronics and other potential applications [30, 36].

On the other hand, due to the out-of-plane quantum confinement in the2D TMDCs, isolated defects from them could serve as single-photon emitters.Four independent studies reported single photon emission from defects inthem in the same period [74–77]. Figure 1.7(a) shows one example of thePL mapping of the quantum emitters from the monolayer. The emissionlinewidth of these quantum emitters is quite narrow (~0.1 meV), comparedto the broad linewidth of the free exciton emission (~10 meV), as shown inFig. 1.7(b). Photon antibunching features from time-correlation measurementsshow that these emitters are indeed single-photon emitters [Fig. 1.7(c)]. Inter-estingly, under finite magnetic field, the spectral wandering from the doublet

16 Introduction

Figure 1.6: Broad tunability of PL from 2D TMDCs. (a) PL from a monolayer MoS2 com-pared to that from a bilayer. The inset shows how the PL intensity decreases withincreasing number of layers [35]. (b) Absorption (left panel) and PL (right panel)spectrum of a monolayer MoS2 under tensile strains up to 0.52% along the zigzag di-rection [97]. (c) PL from a monolayer MoSe2 as a function of the back-gate voltage, theXo represents emission from neutral exciton, and the X+ and X− are emission frompositively and negatively charged excitons respectively [54]. (d) Tuning of PL from amonolayer MoS2 by chemical doping. The inset shows the normalized spectra [98].(e) Normalized PL spectra from a monolayer MoS2 for different temperatures [99].(f) PL emission from Mo1−xWxS2 monolayer with different composition x. The peakrefers to the emission from the A and B excitons [100].

.


Figure 1.7: Single-photon emission from 2D TMDCs. (a) PL mapping of isolated quan-tum emitters in a monolayer WSe2 [75]. (b) Typical emission spectrum from thequantum emitters shown in panel (a), it shows much narrower linewidth (~0.1 meV,left inset) than that of free excitons (~10 meV, right inset) [75]. (c) Time-correlationmeasurements showing obvious photon antibunching confirms the single-photon na-ture of the emission shown in panel (b) [75]. (d) Energy splitting between the doubletfrom the quantum emitter as a function of the applied magnetic field [75]. (e) Voltage-dependent quantum emission from a monolayer WSe2, X and Y represent two differ-ent emitters [76]. (f) Spectrally integrated voltage-dependent emission profiles fromthe line X and Y shown in panel (e), here a 5 meV window is used [76].

.

18 Introduction

emission disappear and the extracted Zeeman splitting goes up with increas-ing field intensity, as shown in Fig. 1.7(d), this further confirms that the dou-blet emission is from the same single quantum emitter [74–77]. These emit-ters show advanced emission properties compared to those in self-assembledInGaAs quantum dots [103] and delocalized excitons [104]. Importantly, elec-trical control of the quantum emission has also been demonstrated [76], asshown in Fig. 1.7(e) and (f). In addition, cascaded single-photon emission hasalso been observed from monolayer WSe2 [105], which paves the way for newquantum optical experiments in 2D materials. In particular, single-photonemission was also reported from oxidized WS2 [106] at room temperature.Single-photon emitters with long lifetime and coherence time will play an es-sential role in photonic quantum computing [78,107]. The ’flat’ quantum emit-ters from 2D TMDCs show great potential for such applications. Besides, thesingle-photon emitters embedded in the atomically thin TMDCs are expectedto have better tunability and be more feasible to integrate with other electronicdevices, compared to other solid-state single-photon emitters [36, 108].

What’s more, light-emitting diodes (LED) based on 2D TMDCs have showngreat potential to be used as excitonic emitters, which are based on electron-hole recombination. Different types of LEDs such as Schottky junctions [89],p-n junctions [87, 90, 91] and vertical tunnel junctions have all been demon-strated. Low threshold down to a few nanoamps [80, 87] and external quan-tum efficiency up to 10% [93] make these TMDCs-based LEDs suitable forfuture optoelectronic applications such as chip-integrated emitters. Impor-tantly, emission in these excitonic LEDs is tunable by controlling the injectionbias [87, 93], which makes them attractive for electrical integration. In con-trast, the highest reported emission efficiency of graphene-based LED is onlyaround 0.3%, which is based on thermal radiation of hot electrons [109]. Inaddition, the unique valley-dependent characteristics of 2D TMDCs providethese LEDs with controllable polarization, more about that will be discussedlater.

1.3.2 Valley pseudospin

As discussed previously, the lack of an inversion center and strong spin-orbitcoupling in the electronic structure of 2D TMDCs lead to unique valley-basedphysics and applications [36, 43, 112]. Figure 1.8(a) shows the trigonal pris-matic structure of monolayer TMDCs (upper part), the honeycomb structurewithout center of inversion symmetry and the 2D first Brillouin zone (lowerpart) [36]. The energy-degenerate valleys K and K’ facilitate the valley degreeof freedom and valley-based selection rules, as illustrated in Fig. 1.8(b). Fur-thermore, the spin-orbit coupling splits the spin degeneracy at each valley andlocks the spin and valley pseudospin degrees of freedom: the spin-up state atthe K valley and the spin-down state at K’ are degenerate [26, 36, 43], whichis shown in Fig. 1.8(b) as well. Importantly, this valley degree of freedom isaddressable by optical pumping: pumping with circularly polarized light of


Figure 1.8: Valley properties of 2D TMDCs. (a) Trigonal prismatic structure of mono-layer TMDCs (upper part), the honeycomb lattice structure with broken inversionsymmetry and the 2D first Brillouin zone with the high-symmetry points (lowerparts) [36]. (b) Electronic bands near the K and K’ points, the spin (up and downarrows) and valley (K and K’) degree of freedom are locked together. m is the az-imuthal quantum number [36]. (c) Circular dichroism spectra from monolayer MoS2under circularly polarized light excitation, in which the opposite sign of circular lu-minescence is caused by the valley splitting [47]. (d) Electrical control of circularlypolarized emission from WSe2-based light-emitting transistor. The middle part il-lustrates the contribution to electrolumninescence from two valleys. The lower partshows the circularly polarized electrolumninescence for two opposite current direc-tions, as schematically indicated in the top insets [110]. (e) The source-drain biasvoltage dependence on the Hall voltage for the monolayer MoS2-based transistorunder right (red solid line), left (red dashed line) circularly polarized and linearlypolarized (red dotted line) light modulation. The blue solid line shows the results ofa bilayer device under right circularly polarized light modulation. These results area signature of a photoinduced anomalous Hall effect (AHE) driven by a net valleypolarization [52]. (f) Polarization-resolved SHG measurements for left (σ+) and right(σ−) circular components under σ+ excitation [111].

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20 Introduction

different handedness could populate electrons into a specific valley [46, 47].Figure 1.8(c) shows one example of how optical pumping could address thevalleys and control the polarization of the PL emission [47]. Vice versa, thevalley-dependent optical properties also make it possible to fabricate TMDCs-based LEDs with controllable emission polarization [87,91,110]. In these cases,the electric field at the p-n junctions preferentially pumps the carriers into onespecific valley, depending on the biased field direction, thus the electric fieldcould switch the dominant handedness of the emitted light by changing its di-rection, as shown in Fig. 1.8(d) [110]. Such a TMDCs monolayer p-n junctioncould also be useful in light detection, Figure 1.8(d) shows a transverse valley-polarized current with the illuminated light of different polarization, whichis called photoinduced anomalous Hall effect (AHE) [52]. A light harvestingdevice based on valley polarization has also been demonstrated [80, 113]. Inaddition, the valley degree of freedom and the strong excitonic effects alsoinduce exceptional selection rule in the nonlinear regime, namely, the emit-ted SHG is anti-circular polarized with respect to the excitation [111, 114], asshown in Fig. 1.8(f). What is more, excitonic valley coherence [49], valley-and spin-polarized Landau levels [115] and valley Zeeman effect [116–119]have all been demonstrated in monolayer TMDCs too. Optical [120, 121],magnetic [104, 122] and electrical [49] control of the valley pseudospin in 2DTMDCs have also been developed lately. The dynamic control of valley indexopens up extraordinary opportunities for valleytronics: devices based on con-trol of the electrons’ valley degree of freedom, which is potentially anotherdimension for carrier to encode information [43]. Overall, the valley-spincoupling in 2D TMDCs bring both new valley-associated physical phenom-ena and novel applications [26, 112], which requires more exploration. Asmentioned, the spin-valley coupling also has impacts on the nonlinear prop-erties of the 2D TMDCs, we will discuss more nonlinear characteristics of 2DTMDCs in the following section.

1.3.3 Nonlinear optical properties of 2D TMDCs

The nonlinear optical properties of materials have been applied in wide rangeof applications and are important parts for modern optics [123]. 2D TMDCsalso show exceptional nonlinear responses including SHG [124–126], sum-frequency generation [127], four-wave mixing [127] and third harmonic gen-eration [128, 129]. In particular, SHG from 2D TMDCs due to their symmetrybreaking has attracted a lot of attention, because the ultrathin layer showsstrong SHG considering their atomic thickness [124]. The SHG possessessome extraordinary properties, such as broad tunability [58,114]. Importantly,the ultrathin nature and passive surface of 2D TMDCs make them suitable forintegration with silicon photonics platforms [130,131], which is promising forenabling second-order nonlinearity in the silicon photonics platform, as sil-icon itself does not have such property due to symmetry structure. Moredetails of SHG from 2D TMDCs will be discussed below.


SHG from 2D TMDCs

Figure 1.9: SHG characteristics from 2D TMDCs (a) Power dependence of SHG from amonolayer MoS2, the upper inset shows the fundamental spectra (red) and the SHG(blue). The lower inset shows the layer-dependent intensity of the SHG [125]. (b) Theintensity of the parallel (blue squares) and perpendicular (black circles) polarizationcomponents of the SHG from monolayer MoS2 as a function of the angle between thelaboratory and MoS2 crystalline coordinates [125]. (c) SHG from a monolayer WSe2as a function of 2x energy of the pumping, which reveals the resonant behavior ofthe SHG [58]. (d) SHG intensity from monolayer WSe2 in resonance with the excitonat selected gated voltage [114]. (e) SHG mapping as an effective tool to determine thedifferent grain boundaries of a CVD-grown monolayer MoS2 [132]. (f) SHG mappingused to determine the polytypes of MoS2 ultrathin layers [133].

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22 Introduction

As discussed above, the lack of inversion symmetry in monolayer TMDCsnot only gives rise of exceptional electronic and optical properties, it alsoallows strong optical SHG, which does not exist in its bulk form due to sym-metry [123]. On the other hand, nonlinear optical responses are an impor-tant aspect of light-matter interaction and play an essential role in variousphotonic and optoelectronic applications. 2D TMDCs might offer great po-tential both in the linear and nonlinear regime, considering their superiormechanical, electronic and optical properties, as well as flexibility for inte-gration [36, 112, 130]. Intense SHG have been demonstrated from differentmaterials such as MoS2 [124, 125, 134], MoSe2 [135], WS2 [136]. Figure 1.9(a)shows one example, the SHG from monolayer MoS2 and its dependence onthe power and layer number [125]. The parallel and perpendicular compo-nents of the SHG (refer to the excitation laser polarization) show a six-foldpattern as a function of the angle between the laboratory and the MoS2 arm-chair axis, as shown in Fig. 1.9(b). This pattern reflects the 3-fold-rotationalsymmetry of the crystal structure [125, 134]. Interestingly, the SHG intensityfrom monolayer TMDCs could be tuned by the pumping wavelength dynam-ically (resonant or non-resonant to the exciton transition) [58] [Fig. 1.9(c)] andelectric gating [114] [Fig. 1.9(d)]. This tunability might enable new approachesto optical signal processing. What’s more, nonlinear optical imaging has beenshown as an all-optical way to determine the crystal orientation of 2D TMDCsat a large scale [132] and bring a reliable tool to probe the structure featuresof 2D TMDCs [133], as shown in Fig. 1.9(e) and (f), respectively. All thesenonlinear features of 2D TMDCs show great potential for future photonicapplications.

1.3.4 Challenges facing 2D TMDCs for photonic applications

Though 2D TMDCs possess extraordinary optoelectronic properties and showgreat potential for applications in photonics, such as light-emitting device, anumber of challenges still remain. Firstly, the PL quantum yield from mono-layer TMDCs measured so far is much lower than the expected value for adirect-gap semiconductor. For example, the value reported from monolayerMoS2 is only around 0.004 [35]. Secondly, the atomic thickness of such 2DTMDCs restricts their interaction length with light, which limits some appli-cations and the efficiency. Besides this, controlled large-scale growth is alsoone of the main challenges, but it is beyond the scope of this thesis.

To address the challenge of the limited emission efficiency in 2D TMDCsespecially in monolayer form, in this thesis, we develop the solutions to in-tegrate 2D TMDCs with photonic nanostructures to boost their emission effi-ciency and further control other properties. The reason we choose this methodis due to that various photonic nanostructure including plasmonics [137],waveguides [131], nanoantennas [138, 139] and photonic cavities [140] couldeffectively manipulate light-matter interaction at nanoscale with great flexi-bility. Indeed, integration of 2D TMDCs with photonic nanostructures has

§1.4 Integration of TMDCs with photonic nanostructures 23

shown great potential for enhancing the performance of 2D TMDCs and isalso crucial for future photonic circuit applications [30, 36, 112]. In the fol-lowing section, we will firstly discuss the general principle of integration 2DTMDCs with photonic nanostructures, then some examples of integration of2D TMDCs with photonic nanostructures will be given to illustrate the brightprospect of this method.

1.4 Integration of TMDCs with photonic nanostructures

1.4.1 Purcell effect and emission enhancement

The spontaneous emission rate of an emitter not only depends on the inherentproperties of the materials, but also on the electromagnetic environment itinteracts with, which is well known as the Purcell effect. Thus, we couldmodify the emission rate through changing the environment. Purcell madethe first proposal to put atom inside cavities to enhance its magnetic transitionin 1946 [141].

To describe the modification of the emission rate, we use the quantifiedterm Purcell factor. It is defined as the ratio between the modified and thefree-space emission rate. For an emitter whose transition frequency alignswith the cavity resonance and has a narrower linewidth compared to the res-onance width, when the emitter locates at the maximum field in the cavitymode and the dipole moment aligns with the polarization of cavity mode, thePurcell factor Fp is [142–144]

Fp =Γg

Γ0=

3Qλ3

4π2V0(1.6)

where Γg and Γ0 are the emission rate in the cavity and free space, respectively.λ is the wavelength of transition, Q is the quality factor of the cavity, V0 isthe volume of the cavity mode. This equation tells that we need resonatorsthat could confine light into small volume and keep it for a long time tomodify the emission rate significantly. However, the two requirements forresonators seems contradictory since better confinement usually accompanieswith higher loss. The research of modification of spontaneous emission ismostly about developing better trade-off between these two aspects [144].

Metal nanoparticles and photonic crystal cavities are the two most com-monly used resonators to enhance the emission from emitters. In metalnanoparticles, the light field could be confined beyond the diffraction limitthrough coupling to electron oscillation, or plasmons, in metals. With thedevelopment of nanofabrication techniques, nanoparticles of different geome-tries and smaller size have been designed to achieve better confinement of

24 Introduction

Figure 1.10: Examples of photonic resonators. Schematic designs of plasmonic nanopar-ticles of different geometries: bar (a), cube (b) and bowtie (c). Photonic crystal cavitiesworking on modes of different types: planar (d), vertical (e) and optomechanical (f).The colored dots refer to modes confined by these resonators.

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light. Figure 1.10 shows a few examples of these designs, such as bar (a),cube (b) and bowtie (c). With plasmonic metal nanoparticles, the optical fieldcould be confined in the scale of down to 10 nm, and even smaller modevolume could be obtained by confining light in the gaps between nanoparti-cles [145]. However, the cost we need to pay for such strong confinement isthe high damping loss from metals. The quality factor of the plasmonic metalnanoparticles is in the order of ten [146]. In contrast, photonic crystal cavitycould achieve quality factors as high as millions [140]. But photonic crystalcavity works on the principle that light is confined due to reflections enabledby the periodic dielectric structures. Thus the mode volume of these cavitiesis limited by the diffraction limit, which is around 0.1(λ0/n)3. Here λ0 is thefree-space wavelength, and n is the refractive index of the medium. Variousphotonics crystal cavities have been developed to perform improved enhance-ment of emission. Figure 1.10 also shows a few examples of these designed onplanar (d), vertical (e) and optomechanical (f) modes. In addition, we couldalso use photonic structures to concentrate or increase the absorption of theexcitation light to enhance the emission from emitters, so photonic structureswith multiple resonances could be applied to boost both the excitation andemission processes to achieve best overall light harvesting.

What is more, by coupling to different types of modes excited in the plas-monic nanoparticles or dielectric cavities, other radiation properties of emit-ters, such as directionality and polarization, could be well controlled too.Thus, integration of emitter with photonic nanostructures is a promising wayto control the emission properties of emitters and further enable practical op-toelectronic applications.

§1.4 Integration of TMDCs with photonic nanostructures 25

1.4.2 Control of light emission from TMDCs through photonic integration

Figure 1.11: Coupling of 2D TMDCs with photonic cavities. (a) Integration of a mono-layer WSe2 with a photonic crystal cavity. The WSe2 exciton energy and the cavityresonance are aligned [147]. (b) Polarization-resolved spectra, taken from the deviceshown in panel (a), demonstrating the laser emission [147]. (c) Exciton-polariton dis-persion in a monolayer MoS2-microcavity system measured through angle-resolvedreflection spectroscopy. The dashed red line shows the exciton energy, solid redlines trace the dispersion of the cavity polariton modes [148]. (d) Dispersion re-lation extracted from the measurements shown in panel (c). The red spheres andsolid black lines are the polariton energy and their theoretical fits respectively, whichshows a Rabi splitting of 46 meV [148]. (e) Micro-PL mapping of the monolayerMoS2-nanocavity device. The region 3 corresponds to the defect area in the photoniccrystal cavity, where we could observe obvious PL enhancement compared to otherregions [149]. (f) The spectra taken from the 4 different regions, as shown in panel(e) [149].

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26 Introduction

The atomically thick 2D TMDCs have naturally passivated surfaces with-out any dangling bonds, which makes them suitable to integrate with pho-tonic structures, including planar photonic crystal cavities [147, 149, 150], op-tical microcavities [148, 151], optical ring resonators [152] and so on. Lasingwith low threshold has been demonstrated by integrating 2D TMDCs withphotonic cavities [147, 151], one example is shown in Fig. 1.11(a) and (b). Po-laritons from strong coupling between 2D TMDCs and cavity modes havealso been observed in different systems [148, 151], one of such observationis shown in Fig. 1.11(c) and (d). Besides, a photonic cavity could effectivelyenhance and shape the PL from 2D TMDCs [149, 150], Figures 1.11(e) and (f)show one example.

These cases listed above justify that light-matter interaction in 2D TMDCscould be effectively enhanced and controlled through integration with pho-tonic nanostructures. However, there is a lot more to explore in this field,especially considering the great flexibility and potential offered by photonicstructure. For example, what is the crucial factor that affects the light emissionperformance when integrating 2D TMDCs with various photonic structuressuch as plasmonics? How to extend the light-matter interaction length for 2DTMDCs through photonic integration? How to design the proper structureto manipulate the valley properties? In this thesis, we are exploring novelmethods to control and manipulate light-emitting properties of 2D TMDCsby integration with photonic platforms.

1.5 Motivation and thesis outline

2D TMDCs show great potential for optoelectronic applications especiallyto be used for a future versatile tunable light source including novel LEDs,’flat’ emitters and low-power laser, as discussed in Section 1.3. However, thePL quantum yield of these materials are far lower than expected for direct-bandgap semiconductor and the atomic thickness intrinsically limits the light-matter interaction length, which prohibits them from realizing many practicalfunctionalities. Integration with resonant photonic nanostructures is promis-ing to enhance the emission from such 2D TMDCs and further engineer theiremissive properties such as polarization and directionality, which are crucialfor lots of practical applications. Though some work has been done aboutintegration of 2D TMDCs with photonic structure, it is far from enough andthere is still a lot to explore. In this thesis, we focus on developing novelphotonic platforms to enhance and engineer the emission from monolayerTMDCs including plasmonic structures, waveguides and nanoantennas.

Localized plasmon resonances are known to be good for controlling lightemission from nanoemitters due to high Purcell effect, thus could offer goodmeans to manipulate emission from 2D TMDCs. In Chapter 2, we demon-strate the integration of monolayer MoSe2 with a resonant plasmonic nanoan-

§1.5 Motivation and thesis outline 27

tenna array, and show full control of the PL from strong enhancement toquenching through changing the spacer thickness between the nanoantennaand the monolayer MoSe2. Our simulations further reveal the crucial factorthat affects the PL performance of the plasmonic-monolayer-MoSe2 system.When we published our work, this was the first demonstration of MoSe2-plasmonic integration and showed great control of the emission.

Though plasmonic structures could effectively manipulate the light emis-sion from 2D TMDCs, the enhancement relays on local hot spot, hence it iscrucial to control the distance between the plasmonic structure and the mono-layer TMDCs precisely, if we want to harvest the emission, as learned fromthe experiments in Chapter 2. The distance is usually in nanometer scale andhard to implement in practice. Furthermore, the gold or silver plasmonicstructures are not compatible with silicon platform widely used in modernphotonics. To address this issue, in Chapter 3, we demonstrate a monolayerWSe2-loaded waveguide-grating system based on the silicon photonics plat-form. This Si-based system supports multiple resonances, originating fromdifferent modes supported by the waveguide. This enables us to combine theexcitation and emission enhancement at the same time. What is more, thissystem could effectively guide the emission components of different polariza-tion from WSe2 into different directions, which is induced by the dispersionof the grating for different modes. The platform demonstrated here could beused for a chip-integrated multi-functional light source, as well as for appli-cations such as visible light communication.

Valley polarization in 2D TMDCs inspires lots of new physical phenom-ena and shows great potential applications in valleytronics, such as informa-tion encoding. In Chapter 4, we propose a TMDCs-nanoantenna scheme thatcould effectively route emission from different valleys into opposite direc-tions spatially. By mimicking emission from monolayer TMDCs as circulardipole emitters, we demonstrate numerically that a simple two-bar plasmonicnanoantenna could realize such functionalities. The directionality derivesfrom the interference of the electric dipole and quadrupole modes excited inthe nanoantenna. Thus, we could tune the emission direction of such TMDCs-nanoantenna system by just choosing to address different valleys (changingthe polarization states of the pumping). Such TMDCs-nanoantenna showsgreat potential for applications like information encoding and processing.

Monolayer TMDCs possess intense SHG due to inversion symmetry break-ing and show lots of potential applications in the nonlinear regime. Espe-cially, they are suitable candidates for integrating with Si photonics platformwithout any lattice-mismatch issues (a problem for conventional III/V mate-rials). Such integration could enable many second-order nonlinear function-alities in silicon photonics, because silicon itself does not have second-ordernonlinearity due to the symmetric structure. However, the nonlinear inter-action length of 2D TMDCs is limited by the subnanometer thickness, thusthe overall nonlinear conversion efficiency is low. To overcome this issue,

28 Introduction

in Chapter 5, we demonstrate integration of monolayer MoSe2 onto siliconwaveguide. By pumping the monolayer MoSe2 through the guided modes,we achieve around 5 times enhancement of the SHG compared to excitationfrom free space. This enhancement is due to the fact that the waveguide con-figuration dramatically increases the nonlinear interaction length and allowsfor phase matching between the fundamental and second-harmonic fields .Furthermore, our theoretical calculations reveal how the internal mode con-version works and points out future directions to achieve better nonlinearperformance. This work demonstrated here shows that the limited interac-tion length of 2D TMDCs could be effectively extended by waveguide inte-gration, which opens door to many on-chip applications such as spontaneousparametric down conversion and parametric amplification.

In Chapter 6, we summarize the work that have been done and discussabout the possible future directions and outlook.

Chapter 2

Manipulation of PL from 2D MoSe2by plasmonic nanoantenna

2.1 Introduction

As discussed in Chapter 1, 2D TMDCs have lots of advanced properties andshow great potential for future optoelectronic applications [30,36,43,112]. Es-pecially, in photonics, these atomic materials are promising to be used asversatile light-emitting source as presented in Section 1.3. However, the PLemission efficiency of such 2D materials is much lower than we expect for a di-rect gap materials [35], which limits many practical applications. On the otherhand, novel integrated devices utilizing the properties of TMDCs have beendemonstrated, including ultra-sensitive photodetectors [79] and low thresh-old lasers [153]. In the latter, the interaction between TMDC and a photoniccrystal cavity emphasizes the importance to enhance the emission from such2D semiconductors through interactions with photonic nanostructures.

Emission from quantum emitters could be well controlled by localizedplasmon resonances (LPR) sustained by metallic particles due to high Purcellenhancement [137, 141]. As such, the hybrid systems of plasmonic nanoparti-cles with 2D TMDC materials have been a subject of intense interest. By thetime our work came out, research in hybrid systems composed of plasmonicnanostructures and TMDCs had mainly focused on MoS2. Effects such asphotocurrent enhancement [Fig. 2.1(a)] [154], PL enhancement by plasmonicgold nanoantenna [155] and nanoshell structure [156] have been demon-strated[Fig. 2.1 (b) and (c)]. In the work shown in Fig. 2.1 (b), they demon-strated around 65% PL enhancement and peak shift, which were attributedto the plasmonic enhanced optical absorption and subsequent heating of theMoS2 monolayer [155]. In the work shown in Fig. 2.1 (c), the PL enhancementeffect was also mainly due to the enhanced optical absorption [156]. After-wards, plasmonic cavity coupled to both the excitation and emission was alsodesigned to achieve better PL enhancement from monolayer MoS2 [157, 160],Figure 2.1 (d) shows one example of the plasmonic cavity with double res-onances [157]. Besides, plasmonic bowtie antenna with Fano resonance was

29

30 Manipulation of PL from 2D MoSe2 by plasmonic nanoantenna

Figure 2.1: Control of monolayer MoS2 properties by plasmonic. (a) Photocurrent en-hancement induced by plasmonic gold nanoparticles from a monolayer MoS2-basedtransistor [154]. (b) PL enhancement from a monolayer MoS2 through integrationwith resonant plasmonic gold bars. Left: MoS2-gold hybrid structure, right: 2D PLmapping of the system [155]. (c) Spectra of a monolayer MoS2 with (green) andwithout (red) gold nanoshell deposition on top [156], the inset shows the scatteringspectrum of the gold nanoshell. (d) Schematic image (left) and mode profiles (right)of double resonant plasmonic cavity designed to enhance the PL from a monolayerMoS2 [157]. (e) Reflection spectrum from a bowtie plasmonic antenna-MoS2 hybridsystem showing Fano resonance [158]. (f) Pl quenching effect from a gold-MoS2 hy-brid system [159].

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§2.1 Introduction 31

also demonstrated to control the emission and reflection of monolayer MoS2[158] [Fig. 2.1 (e)]. What’s more, atomic-scale morphological detection [161],and nanophotonic circuit composed of a single silver nanowire and MoS2flake [162] have been studied too. Plasmonic enhancement of PL has alsobeen explored in WS2 monolayers (PL at shorter wavelengths of ≈620 nm)by coupling to gold nanoparticles [163]. However, in a number of these ex-periments, the inter-band absorption peak of gold (500–600 nm) could likelyhave affected the enhancement effect. While there are other members in theTMDCs family with emission in the infrared range (away from gold enhancedinter-band absorption) remained unexplored, such as MoSe2. Besides, most ofthese experiments demonstrated emission enhancement of TMDCs as a com-bination from excitation and emission processes. Compared with enhance-ment in the excitation process, enhancement in the emission is more robustas it does not depend on the pumping scheme, which is especially importantfor electronically pumped emitting devices. More thorough investigation isdesired in this respect.

Interestingly, the inverse effect namely PL quenching, has also been re-ported when investigating a Au-MoS2 hybrid system [159]. They attributedthe quenching to the charge transfer from the monolayer MoS2 to the goldnanoantennas through the resulting Schottky barrier of 0.4 eV. However, thequenching of PL emission from the monolayer should also happen at verysmall distances between the antennas and the TMDC due to the coupling ofthe emitted photons into non-radiative plasmonic resonances of the nanoan-tennas, i.e. dark plasmonic modes [164]. Nevertheless, the control of PL from2D materials in the full range from PL quenching to enhancement by varyingthe coupling to the plasmonic antennas (through the variation of the spacingto the TMDC) remains so far not explored.

Here, we study the coupling between a monolayer MoSe2 and gold nanoan-tenna arrays mainly focusing on emission process. PL manipulation fromquenching to enhancement was realized by changing the thickness of a spacerused to spatially separate the 2D material and the antenna arrays. Numeri-cal simulations support our observed phenomena and reveal the couplingmechanism in this hybrid system. MoSe2 is used here because it has somesuperior properties compared with well studied MoS2, though both are ofsimilar structure. Firstly, MoSe2 exhibits a smaller bandgap, higher elec-tron mobilities, higher internal quantum efficiency, and much narrower linewidth compared to the extensively studied MoS2 [165–167]. These intrin-sic characteristics imply different applications compared to MoS2. Secondly,few-layer MoSe2 possesses a nearly degenerate indirect and direct bandgap,which makes it more suitable for external modulation of bandgap and op-tical properties [165]. Thirdly, the direct bandgap of MoSe2 is close to theoptimal bandgap value of single-junction solar cells and photoelechemical de-vices [167]. Importantly, MoSe2 has a lower Fermi energy level (4.4 eV) [168],resulting in reduced charge transfer when in contact with gold. While MoSe2is an appealing candidate for coupling to gold plasmonic nanostructures with


PL in near-infrared range (away from gold’s enhanced dissipation due tointer-band transitions), this has remained unexplored to date.

2.2 Plasmonic nanoantenna design and sample fabrication

The emission of TMDCs could be generally altered by metal particles, such asthese used in our experiments, in two ways. Namely, enhancing the local fieldin the excitation process or the local density of states in the emission process,at the location of the nanoemitter. Whereas the first effect directly translatesto an increase of the excitation rate, the latter modifies the spontaneous emis-sion rate. Such modification of the spontaneous emission rate is commonlyreferred to as the Purcell effect [141]. Generally, modification of the sponta-neous emission rate is more robust way for controlling the emission of suchTMDCs as it does not depend on the pumping scheme, which is especially im-portant for emitting devices that are electronically pumped. However, placinga nanoemitter close to a metal particle also creates additional, non-radiativechannels due to the dissipative nature of metals at optical frequencies. Thisbasically happens when the emitter couples to the higher order plasmonicmodes that are non-radiative in nature. When an emitter is located too closeto the antenna, the non-radiative relaxation rates can dominate, spoiling thebenefits of the radiative decay rate enhancement introduced by the plasmonicnanoantenna. This competing process in the weak pumping regime can bequantified by the quantum yield, defined as the ratio between the radiativeand total decay rates. PL modification, the readily measurable quantity thatis commonly used in experiments, thus relies on a combined consideration ofthe excitation rate enhancement and the quantum yield [164, 169–175]. Thegoal of our experiments is to investigate these processes especially regardingthe emission part in a system composed of plasmonic gold-bar nanoantenna,and a monolayer of MoSe2.

Figure 2.2: The key step-to-step fabrication procedures for gold plasmonic nanoan-tenna. The glass substrate is 100 µm and is cleaned by aceton andisopropanol before ITO coating. The dimensions are not to scale.

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§2.2 Plasmonic nanoantenna design and sample fabrication 33

Figure 2.3: Photographs of the samples with/without spacer. (a and b) Schematicside view of the two samples, without spacer and with spacer respectively.(c and d) The corresponding SEM images of the two samples used in exper-iments. PL spectra of spots a in the region of MoSe2-on-antenna and b inthe region of MoSe2-on-substrate are shown and compared in Fig. 2.4(c) and(d). (e and f) Magnified SEM images of the area bounded by dashed rectan-gles in (c) and (d) accordingly showing the shape of the antenna and how themonolayer flakes are positioned on antennas. The antenna length for the sam-ple without a spacer is 127 nm and 100 nm for the sample with a spacer.

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Rectangular gold nanoantennas with fixed width and height, both of 40 nm,and varying lengths in the range 70− 130 nm were prepared and arranged ina square lattice with a center to center distance between adjacent elementsof 505 nm. The nanoantennas were fabricated by standard electron beamlithography (EBL). The key step-to-step fabrication procedures of these plas-monic nanoantenna is shown in Fig.2.2. In step 1, a A 10 nm indium tin oxide(ITO) was coated by physical sputtering on the glass for conducting and ad-hesion purposes before we start our lithography process. In step 2, we spincoated PMMA495A4 resist with two consecutive produces, 500 revolutionsper minute (rpm) for 5 seconds for photoresist spreading and ]4000 rpm for1.5 min for coating, both at acceleration of 1200 rpm/s. Then post bakingis applied to the sample at 180 ◦C for 3 minutes, the resulting photoresistlayer thickness is around 200 nm. In step 3, we perform EBL using Raith 150(voltage of 20 kv and aperture of 7.5 µm). After electron-beam exposure, de-velopment is performed using cold 1:3 MIBK to IPA with a development timeof 35 s, followed by a rinse in isopropanol for 30 s. After development, in step4, thin layer of Titanium (around 3 nm) and gold (40 nm) are slowly depositedby Electron Beam Thermal Evaporation. In step 5, sample are immersed intohot acetone to remove the unwanted part to form the designed structures.

After characterizing the transmittance spectra of these samples, some sam-ples are coated with a thin layer silica by physical sputtering. The layer thick-ness was measured by ellipsometery. Such an antenna was chosen becausetheir two different localized surface plasmon can be selectively excited byusing different optical polarizations. Next, single layer of MoSe2 sampleswere mechanically exfoliated from the bulk crystal and transferred onto thesample containing the plasmonic nanoantennas. The plasmon resonance ofthe antenna array is around the MoSe2 PL peak at ≈ 785 nm. At the sametime, a second set of samples with slightly lower resonant wavelengths werecoated with a thin layer silica spacer of 8.5± 1.5 nm through physical sput-tering (the thickness is measured by an ellipsometer after the coating). Theresonant wavelengths slightly red shifted due to the coverage, because of theincrease of the surrounding refractive index as experienced by the localizedsurface plasmon polaritons. This sample was designed such that the plas-mon resonance spectrally coincides again with the the MoSe2 PL peak afterapplication of the spacer layer. Then another piece of exfoliated monolayer ofMoSe2 was transfered onto the spacer-coated sample. For reference purposes,we let the monolayer flakes on both samples sit partly on the antenna arrayand partly on the silica substrate coated with a thin layer of indium tin oxide.The schematic pictures of our two samples are shown in Fig. 2.3(a) and (b),respectively and the corresponding SEM images are given in Fig. 2.3(c) and(d). Figure 2.3(e) and (f) show the gold nanoantennas and how the mono-layer flake is positioned on the sample accordingly. The morphology of theTMDC on the nanoantennas was also tested by an AFM measurement in anon-contact mode, which reveals the conformal coating of the monolayer ontop of the antennas.

§2.2 Plasmonic nanoantenna design and sample fabrication 35

Figure 2.4: Spectra properties of the samples.(a) Transmittance profiles of the samplewithout spacer obtained by white light spectroscopy, the electric field of the illumi-nation is polarized along the antenna long axis (solid blue line) and perpendicular tothe long axis (dashed black line), respectively. (b) Transmittance profile of the samplewith spacer before (blue line) and after coating the spacer layer (dashed red line),for illumination with its polarization along the antenna long axis. The transmittancefor polarization perpendicular to the antenna’s long axis are identical in this spectralregion before and after coating the spacer layer, as shown with dashed black line.(c) PL spectral profiles of the sample without spacer corresponding to points a (solidblue line) and b (dashed blue line) in Fig. 2.3(c), the legend ‘ant’ here means on an-tenna and ‘sub’ means on substrate (same in the following). (d) PL spectral profilesof the sample with spacer corresponding to points a (solid blue) and b (dashed blue)in Fig. 2.3(d). (e and f) Normalized spectra of c and d, respectively.

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Figure 2.4(a) and (b) show the transmittance spectra of our antenna arrayswith and without spacer obtained by polarized white light spectroscopy, re-spectively. Here we distinguish the polarization of the incident illuminationby its electric field that is either perpendicular or parallel to the long axis ofthe plasmonic rectangular nanoantenna. The experiential setup used to mea-sure the transmittance is shown in Fig. A.2. The spectra show pronouncedtransmittance dips near the central emission wavelength, marked with verti-cal dashed red line, when the polarization is set to be parallel to the long axis.Note that the contrast of the transmittance dips is not high due to the sparsearrangement of the antennas. Importantly, the antenna resonance disappearswhen changing the polarization of the incident illumination to be perpendicu-lar to the antenna long axis (dashed black lines), confirming that the measuredresonances are a consequence of the excitation of LPR in the nanoantennas.To make sure that the MoSe2 flakes used for our samples are monolayers, wemeasure their PL spectra excited by a 532 nm continuous-wave laser. The PLresults are shown in Fig. 2.4(c) and (d), which all show a good agreementwith results for monolayer MoSe2 reported previously [165, 176], thus con-firming that the fakes we used in experiments are monolayers. Furthermore,we have also conducted Raman measurements on the flakes excited by thesame laser wavelength. While less accurate than the PL identification, themeasured first Raman peak of the flakes at 240.8 cm−1 is consistent with theresults for monolayer MoSe2 [165,176]. Therefore, we could conclude that theMoSe2 fakes we used in experiment are monolayers.

2.3 PL characterization

Next we investigate how the spectral profiles of the monolayer MoSe2 areaffected by the nanoantennas. Micro-PL spectroscopy and micro-PL spa-tial mapping was performed using a commercial WiTec alpha300S systemin scanning confocal microscope configuration as shown in Fig.A.3. For ex-citation, light from a supercontinuum laser with 5 nm spectral bandwidthtunable in the range 530 − 640 nm is focused on the sample with a 100×objective (NA=0.9) from the MoSe2 side. The measured spot size of the exci-tation beam is ∼ 1 µm at 532 nm wavelength. The MoSe2 PL is then collectedfrom the substrate side of the sample using a 50× (NA=0.65) objective (trans-mission mode). A linear polarizer inserted into the detection path allows forselectively collecting the PL for different polarizations. In order to remove thelight of the exciting laser source from the signal, a 715− 1095 nm bandpassfilter was introduced. The spectrometer is fiber-coupled to an Ocean Opticsspectrometer using a multimode (non-polarization maintaining) fiber to neu-tralize any possible polarization sensitivity of the spectrometer. To furtherrule out any unwanted effects from possible gold PL, we have tested the PLfrom base gold antennas, which was found to be below the noise level of ourdetection. For spatial mapping, the MoSe2 has been excited with an aver-age power of 0.5 µW, leading to an excitation power density of 637 W/cm2 on

§2.3 PL characterization 37

Figure 2.5: PL emission control by the plasmonic antennas. (a and b) Optical imagesof two samples, without a spacer and with a spacer, respectively. (c and d) Cor-responding typical PL mapping images of the samples integrated over the range715− 1095 nm, both images are normalized to their respective maximum value. (eand f) Corresponding antenna effects varying with collection polarization angles ofthe two samples, measured data (asterisks) and fitting curves (red solid lines). Theinsets in e and f indicate the direction of polarization with respect to the gold rectan-gular antenna.

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the sample. The PL has been collected for different polarizations using anavalanche photodiode in combination with a long-pass filter.

The PL spectra of two typical regions, point a (in MoSe2-on-antenna re-gion) and point b (in MoSe2-on-substrate region) [Fig. 2.3(c) and (d)], usingexcitation of 532 nm, are shown in Fig. 2.4(c) and (d), respectively. The mea-sured PL from the monolayer MoSe2 shows that the PL is quenched for the


sample without a spacer, while it is enhanced for the sample with a spacer.Note that the absolute value of PL signal on MoSe2-on-substrate region inFig. 2.4(d) (sample with spacer) is lower than its counterpart in Fig. 2.4(c)(sample with no spacer). This is likely due to the variation of the sample qual-ity and not due to the spacer material. As already mentioned, our monolayerMoSe2 flakes were exfoliated from bulk crystal, hence the sample propertieslike size and formation may vary from one flake to another. As such, the PLsignal could vary for different flakes. Besides, to obtain proper PL signal inexperiments, we have further adjusted the excitation laser power accordinglyfor different samples. Thus, the comparison of the absolute PL values fromdifferent samples does not represent valuable information. Here we focus onthe comparison of the PL on different parts of the same flake, which excludesvariations of the PL signal from other factors like the sample quality. If thetwo samples we used in experiments were exactly the same, the PL value onMoSe2-on-substrate region shown in Fig. 2.4 would be the same. The normal-ized spectra are also shown in Fig. 2.4(e) and (f) accordingly. The flake on thesample without spacer shows slightly red-shifted and broadened spectrumon the antenna compared with the PL spectra on the substrate. The origin ofthe quenching effect cannot be unambiguously identified here, however it islikely due to the ohmic losses [164] as well as possible additional charge trans-fer effect [159], as the flake is in direct contact with the antenna. The changesof spectral position and intensity are relatively small compared to MoS2 [159],suggesting that the charge transfer is not as strong as in MoS2, which is sup-ported by the larger Schottky barrier of 0.7 eV [159,168]. Therefore, we believethat the dominant reason for quenching is the increased non-radiative decayof the emission from the MoSe2 in close proximity to the gold antennas.

In contrast, the sample with a spacer shows almost the same spectral shapeof emission for both MoSe2-on-antenna and MoSe2-on-substrate regions asshown in Fig. 2.4(f), which is different from the results of broadened andred-shifted spectra reported in the literature [155, 160] about MoS2. This is astrong indication that the stronger PL on MoSe2-on-antenna region is mainlycaused by emission enhancement and implies increased radiative decay dueto plasmonic coupling in our system. Otherwise ohmic effects brought bythe excitation enhancement will broaden and shift the spectral profiles [155].Moreover, this unchanged spectra with enhanced intensity characteristic ofthis system is particularly beneficial for practical devices based on MoSe2when considering its stability, as well as some optical applications that requirestationary spectrum such as interferometry.

To further understand the influence of the antenna on the PL, we map the2D PL image integrated over the spectral region 715− 1095 nm. The opticalimages of the two flakes are shown in Fig. 2.5(a) and (b), accordingly andthe results of PL mapping are shown in Fig. 2.5(c) and (d) (both images arenormalized to the corresponding intensity maximum), respectively. Both, thequenching effect for the sample without spacer and the enhancement for sam-ple with spacer can be clearly seen there. We can also see that the emission

§2.4 Numerical modeling 39

from the gold antenna or the substrate regions is negligible as compared to theregion covered by the monolayer MoSe2 flakes, which means the backgroundis negligible.

In the following, we define the quantitative PL change due to couplingwith antenna, called here antenna effect, as PLant/PLsub. This quantity iscalculated by taking the average PL value of a small area from the MoSe2-on-antenna region then subtracting the corresponding background and nor-malizing to the PL from the same area at MoSe2-on-substrate region, namely( 1© - 2©) / ( 3© - 4©), as shown in Fig. 2.5(c) and (d). It can be seen from thedefinition that the antenna effect would be greater than 1 for PL enhancementwhile less than 1 for quenching. We also collect the PL at different polariza-tions by adding a polarizer in the collection pathway and obtain the antennaeffect varying with polarization angles, as shown in Fig. 2.5(e) and (f) forboth samples, respectively. We observe approximately threefold maximal en-hancement of the PL from the MoSe2 monolayer for the sample with a spacer,while nearly up to fourfold quenching for the sample with no spacer. Theantenna effects are obviously polarization dependent for both samples due tothe excitation of the dominant LPR along the long antenna axis. We note thatin our measurements we cannot clearly distinguish the individual antennaspatially, hence our measurements represent the average quantity of enhance-ment across the entire unit cell of the antenna array. This averaging reducesthe effective enhancement/quenching effect, which can be much greater forsome positions of the emitters (see the Numerical Modeling section below).Besides, the strongest enhancement effect happens when the polarization isalong the antenna’s long axis, which reflects the intrinsic property of LPRresonance along the long axis.

To investigate the interaction mechanisms of these hybrid systems in moredetail, we measured the antenna effect variations with respect to differentpumping wavelengths using a supercontinuum laser tunable in the range of530-640 nm. No significant dependence was found in the PL emission byvarying the excitation wavelength by more than 100 nm. This excitation wave-length insensitivity implies further that the observed phenomena are mainlyinduced by interaction between the antenna and MoSe2 during emission pro-cess, and the excitation does not affect our measurements much. This behav-ior is confirmed in our numerical modeling part below.

2.4 Numerical modeling

To support our experimental results and further understand the nature ofthe involved processes, we perform numerical calculations. The numericalcalculations also allow us to see the effects of fine variation of the spacerthickness, which is not possible in our experiments due to the percolation ofthe dielectric spacer on top of the antenna for small thicknesses (< 6 nm).


Figure 2.6: Schematic representation of the simulation. (a) Schematic of the model struc-ture. On the left we show a dipole emitter (red arrow) above a metallic nanoantennawhere the distance has been controlled with a spacer. On the right we show the ref-erence situation that is geometrically the same except the antenna is missing. (b) XZcross section of the simulation setup, d indicates the spacer thickness, the coordinatesare consistent with the one shown in a. (c) The enhancement of the electric field bythe antenna, normalized to the reference case, calculated in a XY plane 7 nm abovethe antenna. The antenna (top view) is excited by a plane wave of the wavelengthλ = 532 nm, polarized parallel to its short axis. The strongest field enhancementappears at the edges of the antenna.

.

Finite Element Method (FEM) solver, as implemented in the commerciallyavailable software package COMSOL, were used to perform the numericalcalculations. The simulations were performed with open boundary condi-tions. To analyze the emission properties, an electric dipole emitter is placedin the computational domain and its emitted field has been calculated ev-erywhere in space. The radiative decay rate was calculated by integratingthe outward, normal component of the normalized Poynting vector througha surface surrounding the antenna and the dipole emitter. The total decayrate took the non-radiative losses into account, which are calculated by in-tegrating the Ohmic losses across the volume of the antenna. Both energiesrequire a normalization to the energy emitted by the same source into thesame background material.

The antenna considered here has both width and thickness of 40 nm anda length of 127 nm. The length was tuned to be resonant at the emissionwavelength of λ = 785 nm. To avoid nonphysically sharp edges, we modelthe antenna as rounded with a radius of curvature of 10 nm. The consideredgold properties are based on experimental data from [177] for the permittivityof gold in the visible/near-infrared spectral region. The thickness of the ITOis set to 10 nm and its refractive index is taken from [178]. The glass substrate(SiO2) is modeled as a half-space and has a constant refractive index of n =1.44. To avoid numerical artifacts, a minimum distance of 2 nm between thedipole emitter and the ITO or the antenna, respectively, is introduced.


To analyze the emission process, the interaction of an electric dipole emit-ter and the antenna is considered in the weak coupling regime. We performcalculations for both cases: once for an emitter coupled to the gold antennaand once for an emitter on a glass substrate for reference. To study the ex-citation process, the setup with and without the antenna is irradiated with aplane wave at a wavelength of λ = 532 nm. The polarization of the electricfield is set to be parallel to the short axis of the antenna, corresponding to ourexperimental arrangement. We solve numerically Maxwell’s equations andobtain spatially resolved electro-magnetic field at the excitation wavelength.Equating the results for the excitation and the emission processes once in thepresence of the nanoantennas and once in the referential situation allows fordirect comparison with our experimental measurements as the method usedin [164]. All geometrical details considered here are consistent with the ex-periments.

In slightly more detail, the normalized excitation rate can be calculated as

γexc/γ0exc =

∣∣[np · E(rm)]/[np · E0(r0)]∣∣2 (2.1)

where np is the unit vector pointing in the direction of the dipole moment andrm is the location of the dipole emitter. The fields E(rm) represent the inducedelectric fields at the location of the dipole emitter in a setup with antennaunder plane wave illumination, and E0(r0) is the referential induced electricfield on the surface of the substrate in a setup without antenna under sameillumination. The emission is a result of the exciton recombination, whichrestricts the electric dipole moment of the emitter to be in the 2D plane of theMoSe2 flake. However the orientation of the dipole moment in this plane isuncertain [179]. We therefore consider an average ’in-plane’ amplitude of theexcitation field at λ = 532 nm and use

np · E(rm) =√

E2x(rm) + E2

y(rm) (2.2)

in the calculation of the field enhancement.

To characterize the emission process, we then calculate the quantum yield.This quantity is a measure for the quality of the antenna, since it accounts forthe non-radiative and internal losses of the hybrid antenna - dipole emittersystem. The normalized quantum yield is given by [180]

qa/q0a =

γr

fl + (1− i)/i· fl0 + (1− i)/i

γ0r

(2.3)

where γr and γ are the radiative and the total decay rate of the emitter,respectively, evaluated at the emission wavelength of λ = 785 nm. The super-script ‘0’ indicates the quantities calculated without the antenna. The quantityηi is the intrinsic quantum yield of the dipole emitter [164, 180]. For a perfect


emitter, it holds ηi = 1 and the antenna can only reduce the overall system ef-ficiency. For emitters with low ηi, the overall radiative efficiency can howeverbe effectively increased. For our simulations, we considered ηi = 0.05 to re-flect the fact that MoSe2 is a rather poor emitter. This quantity is estimated bycomparison of the experimental emission from flakes of MoSe2 and MoS2 [35]on a glass substrate at the same excitation power. The MoSe2 flake shows ap-proximately an order of magnitude higher PL intensity, therefore we estimateits internal quantum efficiency to be a factor of 10 higher than MoS2 [35]. Notethat the quantum yield we used here is just a rough estimation and the actualvalue is unknown so far, eventually we wish to emphasize that a monolayerof MoSe2 is a rather poor emitter. However, the actual value we assume forthe intrinsic quantum yield is of secondary importance considering the factthat a quantitative comparison to the experimental results is not our purpose.This would require spatial averaging of the emission process to reflect the factthat a monolayer MoSe2 covers the entire sparse antenna. And the detaileddiscussion of quantum yield of monolayer MoSe2 is beyond the scope of thiswork. In contrast, here we just want to reveal the physical mechanism behindour observed phenomena.

Finally, the fluorescence rate is a product of the normalized excitation rateγexc/γ0

exc and the normalized quantum yield qa/q0a and is the quantity mea-

sured in the experiment:PLant

PLsub =flexc

fl0exc·qa

q0a

(2.4)

A sketch of the considered geometry is shown in Fig. 2.6(a). Figure 2.6(b)shows the cross section of the simulation setup as well. The enhancement ofthe electric field at the excitation wavelength of λ = 532 nm by the antennain the plane where the MoSe2 flake locates in experiments is displayed inFig. 2.6(c). Here, the antenna (top view) is excited by a plane wave. Note thatthe strongest field enhancement appears at the edges of the antenna.

As mentioned previously, the transition dipole moments of MoSe2 are spa-tially distributed in the plane and the eventual measurement signal is theresult of an ensemble averaging from all the individual positions and orienta-tions in experiments. However, full numerical consideration of such averagingis resource consuming. Furthermore, the averaging will not provide a phys-ical insight on the different mechanisms of PL modifications. Therefore, wechose to provide a qualitative understanding of the experimental results bystudying the interaction of emitters placed at a few individual positions, asshown below. For this purpose, we consider two emitter positions relativeto the antenna: one at a central position and one at a corner. In the follow-ing, we study the dependence of different physical quantities on the spacerthickness, i.e. the distance between the dipole emitter and the antenna. Forsimplicity and without loss of generality, we use vacuum as spacer material.The electric field intensity of a plane wave for the case with and without theantenna for both locations is shown in Fig. 2.7(a). Please note that the exci-


Figure 2.7: Simulation results. (a) The excitation rate of the electric field of a planewave in the characteristic points of the antenna (center [dark blue] and a top-endcorner [green]), normalized to the intensity of a plane wave in a setup without theantenna. The illumination plane wave is polarized along the short axis of the antennaas indicated by the inset arrow. (b) quantum yield, (c) fluorescence enhancement, and(d) radiative decay rate enhancement for a dipole emitter placed above the centerof the antenna and polarized parallel to its long (dark blue) or short (red) axis; thequantities were calculated also for the case where the dipole emitter was placed abovethe top-end corner of the antenna and parallel to its long (green) or short (light blue)axis.

.

tation enhancement rate shows weak trend that it increases with increasingspacer thickness in the figure, this is caused by interference between incidentfield and the back reflection from the substrate, actually this quantity is al-ways around unity for larger spacer thickness beyond the range shown in thefigures. In full agreement with our experiments, the influence of the antennaon the excitation rate is weak. A minor dependency remains and is taken intoaccount, but eventually the excitation field is not significantly modified whencompared to the reference case. This is because the excitation wavelengthis below the plasmonic resonance sustained by the antenna and no notableinteraction is expected nor encountered.

The quantum yield, defined via Equation (2.3) is displayed in Fig. 2.7(b)


and the fluorescence enhancement PLant/PLsub is shown in Fig. 2.7(c). Wecould see from Fig. 2.7(b) that the quantum yield is enhanced and decreaseswith increasing spacer thickness when dipoles are at the corner of the an-tenna for both orientations. When dipole is positioned at the center of theantenna, the behaviors of the dipoles with different orientations are differ-ent. For the dipole oriented along the short axis of the antenna, the quantumyield is quenched and changes slightly with increasing spacer thickness. Forthe dipole orientated along the long axis of the antenna, the quantum yieldis quenched when the dipole is very close to the antenna. Then the quan-tum yield increases with increasing spacer thickness until reaching its peakvalue at a spacer thickness around 7 nm. Afterward, the quantum yield startsdropping and asymptotically reaches unity. As discussed above, the quan-tum yield takes the leading role that affects the fluorescence rate which corre-sponds to the quantity we observed in experiments. So the fluorescence rateshown in Fig. 2.7(c) preserves the trends of the quantum yield with increas-ing spacer thickness except that the curves are flattened a little bit due to themultiplication with the excitation rate. Since the experimental results are aconsequence of ensemble measurements, we could conclude that the quench-ing effects dominate for the sample in the absence of a spacer. In contrast, fora spacer with a finite thickness the enhancement of the fluorescence can beharvested.We could also infer from the simulation results that the optimumspacer thickness for enhancing the PL is around 7nm (close to the value weused in experiments). Increasing further the space thickness will not resultto more PL enhancement as the emitters interacts weakly with the antenna.Considering the fact that actually a large share of emitters will not be exposedto a spatial region in our experiments where the quantum yield is enhanced,the increase in the fluorescence signal by a factor of three (observed in ourexperiments) is quite remarkable.

The radiative decay rate enhancement γr/γ0r is often discussed as the mea-

sure for the gain of light that the dipole emitter will radiate into the far-fieldwhen coupled to the antenna [144]. The radiative decay rate enhancementfor our antenna is shown in Fig. 2.7(d). Enhancements by approximately upto two orders of magnitude can be seen. This enhancement in the radiativerate is eventually the reason for the observed increase in the fluorescence rate.Actually, the excited emitter has multiple decay channels. First of all, a verylikely path for its de-excitation is the internal non-radiative recombination ofthe excitons and therefore non-radiative relaxation due to the low internalquantum yield. This quantity cannot be affected by the modified optical en-vironment. Additionally, the dipole emitter can decay through radiative ornon-radiative processes via the antenna. Crucially, these are the transitionrates that are improved by the plasmonic antenna. The non-radiative decaydue to the antenna is certainly undesirable, but it is a price that must beaccepted to improve the radiative decay rate.

§2.5 Conclusion 45

2.5 Conclusion

We have studied the coupling of monolayer MoSe2 with plasmonic nanoan-tennas and have demonstrated emission manipulation in such materials fromquenching to enhancement mainly through affecting the emission process.This manipulation is achieved by adding a dielectric spacer between the an-tenna and MoSe2 monolayer. Our experimental results are supported by nu-merical calculations, which further reveal the coupling mechanisms betweenthe plasmonic antenna and MoSe2 monolayer. In particular, we have observedthat the nanoantenna enhances the radiation rate when compared to othernon-radiative decay processes, i.e. especially the internal non-radiative de-cay. To harvest this positive aspect of the nanoantenna requires however toenforce the distance between the MoSe2 and the nanoantenna since other-wise quenching would dominate the processes. This has been clearly seenin our experiments and the observation is fully supported by the numericalsimulation. To the best of our knowledge, the present work provides thefirst study of Au-MoSe2 system, offering more insights into the interactionbetween the nanoantenna and monolayer MoSe2. Importantly, MoSe2 is alargely unexplored member of the TMDC family, offering several advantagesin comparison to its widely studied MoS2 and WS2 counterparts. Moreover,the enhanced PL with unchanged spectrum shape is meaningful for practicalMoSe2 applications when considering its spectral stability. Furthermore, PLmanipulation in our experiments is realized by affecting the emission processof MoSe2, this method is more robust as it is independent from the excitationscheme, which is especially important for devices with electrical pumping.Besides, enhancement (quenching) effect varying with excitation wavelengthis also studied. The method presented here in general offers an important wayfor PL manipulation in large dynamic range from quenching to enhancementfor these advanced materials, as well as the opportunity of polarization-basedPL control, both of which are promising for future optoelectronic applicationsand developments.

Statement

This chapter is written based on the work published in the journal paper:Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei, J.; Decker,M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D. N. "Manipula-tion of photoluminescence of two-dimensional MoSe2 by gold nanoantennas".Sci. Rep. 6, 22296 (2016).

In this work, HC led the projects in sample preparation, PL characteriza-tion, data analysis, paper writing. The simulation was done with the help ofER, JS, CR. All other authors contributed to some part of the projects and thediscussion.

Chapter 3

Enhanced and directional emissionfrom multi-resonant WSe2-Sihybrid structure

3.1 Introduction

As discussed in Section 1.3, 2D TMDCs show a great potential as atomic-scaleversatile light sources, as their electronic structure forms a direct bandgapwhen the material is reduced to a monolayer [30, 36, 112, 181]. Various impor-tant applications such as low-threshold lasers [147, 152, 182], single-photonemitters [74–77, 183], excitonic light-emitting diodes (LEDs) [80, 87], cascadedsingle-photon emission [105] and SHG [58, 124, 134, 136, 184, 185] have beendemonstrated with these 2D materials. Furthermore, the valley-based emis-sion properties of TMDCs open a new door for information processing andnovel helical light emitters [46–49]. The optical properties of these emittersare also electrically tunable, which makes them suitable for on-chip circuitintegration.

On the other hand, enabling light sources in the silicon photonics is an im-portant requirement for on-chip optoelectronic applications [186, 187]. Whilesilicon alone cannot generate the required light, integration with other direct-bandgap materials is being sought. Integration of germanium or III-V materi-als on silicon faces technical challenges due to a lattice-constant mismatch anddifferent thermal properties [188]. With the desire to overcome such limita-tions, the integration of 2D TMDCs onto silicon photonic structures emergesas a new promising solution [189,190]. 2D materials are held together by out-of-plane van-der-Waals forces, and can be transferred onto a silicon substratewithout lattice mismatch issues.

However, the emission efficiency of a single layer TMDCs is much lessthan other direct bandgap semiconductors, which is naturally limited byits sub-nanometer thickness (light-matter interaction length), thus prevent-ing monolayer TMDCs from practical applications. Coupling of 2D mate-

47

48 Enhanced and directional emission from multi-resonant WSe2-Si hybrid structure

Figure 3.1: Control of emission from 2D TMDCs by non-metallic structure. (a) PL spec-tra from different position in a system consisting of GaP photonics cavity and amonolayer WSe2, the inset picture show the top view of system and the position in-formation [150]. (b) PL intensity distribution in the in-plane momentum space takenfrom a monolayer WSe2 on and off the photonic crystal cavity [150]. (c) Schematic ofthe proposed silicon-based photonic crystal cavity to enhance the emission intensityand directionality from 2D TMDCs [191]. (d) Simulated confined electric field distri-bution in the plane perpendicular to silicon rod for the structure shown in (c), twofigures show the two in-plane cross-polarized components, respectively [191].

.

rials to photonic structures is a promising approach to enhance the light-matter interaction and tailor the emission radiation properties [36, 112]. In-deed, various plasmonic structures have been explored to enhance and engi-neer the PL and radiation properties from 2D TMDCs [155–157,160,192–194].However, the plasmonic-driven enhancement of emission is very localizedto the hot-spots of the nanostructures, and the average enhancement overthe entire material remains moderate [193]. Furthermore, the localized hot-spots of plasmonic nanostructures make their coupling to 2D materials highlysensitive to the distance between the emitter and structure, often requiringchallenging nanometer-precision positioning. More details could refer toChapter 2. Non-metallic nanostructures, such as photonic crystal cavities,have also been proposed for enhancing the emission from TMDCs monolay-ers [150, 191, 195]. Figure 3.1(a) and (b) show the emission spectra and direc-tionality from monolayer WS2 integrated with a a GaP photonic crystal cavity,respectively [150]. Figure 3.1 (c) show one silicon-based photonic crystal cav-ity that is proposed to enhance the emission intensity and directionality fromTMDCs [191]. Figure 3.1(d) shows the simulated confined electric field from

§3.2 Grating-waveguide fabrication and characterization 49

this structure. However, these schemes rely on cavity modes with a small vol-ume, again showing overall limited enhancement. More importantly, none ofthese demonstrated platforms is directly compatible to the on-chip integrationin modern silicon photonics [131]. A silicon photonics compatible platformto strongly enhance the collective emission of the entire 2D materials and tocontrol its directionality is highly desirable.

Here, we demonstrate enhanced and polarization-selective directional PLemission from monolayer WSe2 by coupling it to a multi-resonant silicongrating-waveguide structure. The multiple waveguide modes supported bythe structure are engineered to provide enhancement at both excitation andemission wavelengths in order to achieve an optimal PL output. The dis-persion properties of these modes further offer feasibility to simultaneouslycontrol the polarization and directionality of the emission. A significant re-duction in radiative emission lifetime of WSe2 monolayer is also demonstratedby time-resolved measurements. Importantly, our approach is fully scalable,Si-based and thus suitable for on-chip integration. The demonstrated schemecould be potentially used to fabricate efficient chip-based light sources for var-ious applications, including single-photon sources for quantum applicationsand ultrafast modulation emitters for visible communication.

3.2 Grating-waveguide fabrication and characterization

By engineering the available photonic modes in the environment, the light-matter interaction strength could be effectively boosted [164]. Generally, thelargest enhancement of the overall PL emission can be achieved when utiliz-ing photonic structures with multiple resonances that couple to both excita-tion and emission radiation. We realize such a scheme through integratinga WSe2 monolayer onto a shallow multi-resonant grating structure inscribedinto a planar silicon waveguide, which supports multiple propagating moderesonances.

The side view of our experimental arrangement is shown in Fig 3.2a. AWSe2 monolayer is positioned on top of a grating etched into a planar waveg-uide made of amorphous silicon (a-Si). The grating periodicity is selectedsuch that both the excitation laser and the emission couple to available waveg-uide modes. The grating structure facilitates coupling of the pump light (fromfree space, as indicated by the arrow) to a waveguide mode, which increasesthe local field intensity at the monolayer position. Thus, the absorption of thepump light by the WSe2 monolayer is increased and translates to higher ex-citation efficiency. The emission of WSe2 also couples into waveguide modessupported by the high-index a-Si layer. Note that due to the amorphousstructure of the silicon layer, it is nearly transparent at the emission wave-length [185]. The coupling of the WSe2 layer to the silicon waveguide reducesthe radiative lifetime of emission, which in turn is extracted efficiently to free


Figure 3.2: Waveguide-grating structure and its characterization. (a) Schematic side viewof the structure under investigation: a monolayer WSe2 is located on top of a gratinginscribed into the planar waveguide. Geometrical dimensions, of course, are not toscale. (b) parameters of the grating-waveguide structure (i) and scanning electronmicroscopy image of a top view of the grating structure used in experiments (ii),part (iii) shows calculated total field profiles at guided mode resonant wavelengthsof the grating-waveguide structure for normal incident plane waves. (c, d) Measuredand calculated transmittance of the grating-waveguide structure for different linearlypolarized light relative to the unpatterned area, respectively. The dashed line showsthe measured emission spectrum of WSe2 monolayer.

space due to the grating structure. Therefore, such an experimental schemeoffers boosting the PL emission simultaneously through the excitation andemission processes. Furthermore, as the emission couples into different leakymodes supported by the grating-waveguide structure, the emission would behighly directional depending on the dispersion of the modes supported bythe structure.

Experimentally, a 200 nm layer of hydrogenated a-Si was deposited ona glass substrate by plasma-enhanced vapor deposition as the waveguidinglayer. The hydrogenated a-Si layer was deposited by plasma enhanced vapordeposition at 250 ◦C. The refractive index and extinction coefficient of the ma-terial was measured by ellipsometry afterwards. Then, the grating structurewas fabricated by electron beam lithography at 20 kV using the positive re-sist ZEP-520A. The development was performed by inserting the sample inton-Amyl acetate. The resulting resist pattern was used as an etch mask fora-Si etching in CHF3/SF6 plasma. The residual resist was removed by oxygen

§3.2 Grating-waveguide fabrication and characterization 51

plasma. Details for the samples fabrication are shown in Fig.A.1. Comparedto crystalline Si whose absorption starts to increase sharply below 1100 nm,hydrogenated a-Si is transparent up to 700 nm owing to high optical bandgapof 1.73 eV [196]. Hence a-Si was chosen in this work because of its low op-tical loss at the emission peak of WSe2 around 750 nm. The refractive indexand extinction coefficient of the waveguide layer were measured by ellipsom-etry methods afterwards. In the next step, a binary grating with periodicityof 214 nm and depth of 50 nm designed to facilitate coupling of waveguidemodes to radiation and excitation was etched into the a-Si layer. The part (i) ofFig. 3.2(b) shows the designed parameters of the grating-waveguide structure(side view), and the part (ii) shows a scanning electron microscopy imageof the top view of the fabricated grating, and the calculated TE0, TM0 andTE1 mode profiles confined by this structure are also shown in part (iii). Fig-ure 3.2(c) shows measured transmittances for different linear light polariza-tions of the patterned grating relative to the unpatterned area for almost nor-mal incidence, the transmittance is measured from setup shown in Fig. A.2.Multiple resonances arising from the excitation of waveguide modes are vis-ible. The black dashed line shows the measured PL emission spectrum ofWSe2 monolayer overlapping with the resonances. Finite-element light scat-tering simulations for normal incident plane waves were done to confirm thenature of the observed resonances, the results are shown in Fig. 3.2(d). Toaccount for the focusing effect introduced by the objectives used in experi-ments, we assume that the incoming pump light has an angular distributionthat follows a Gaussian shape centered around normal incidence with a stan-dard deviation of 2 degrees. The three resonances can indeed be attributed toTE0, TM0 and TE1 modes supported by the underneath waveguide as labeled,which is discussed in detail below. As shown in the figures, the emissionspectrum of the WSe2 overlaps with both TE0 and TM0 resonances. The exci-tation wavelength could be chosen such that the pump laser couples to the TE1waveguide resonance, thereby we could enhance excitation and emission atthe same time. Furthermore, emission out-coupled from TE0 and TM0 modeswill go into defined directions due to their respective dispersive nature andsharp resonance linewidths. Thus, control the emission directionality can beaccomplished by tailoring either the periodicity or polarization. One can ob-serve discrepancies in terms of magnitude and line shapes when comparingthe numerical and experimental results. We associate these discrepancies tofabrication and measurement uncertainties. However, we wish to note thatthe simulation still well reproduces the resonant wavelengths and linewidthsof the waveguide mode resonances, which is of main importance in the work.The general trend of the relative transmittance spectrum is also captured well.

In deducing the coupling efficiency, we examine the calculated extinctionspectra (where extinction is defined as Ext = 1-T0 at normal incidence). Onecan estimate the coupling efficiency by looking into the peak extinction atresonance and comparing it to the background response in the absence ofthe resonant contribution. The extinction plot is given in Fig 3.3 for thegrating-waveguide structure (a) and a planar multilayer reference (b). The


TETM

TM0

TE0

TE1(a) (b)

(c) (d)

Figure 3.3: Calculated extinction and dispersion relation for the grating-waveguide struc-ture. (a, b) Calculated extinction of the grating-waveguide structure for plane waveexcitation from air with TM (a) and TE (b) polarization. (c,d) Dispersion relations atkx = 0 for TM (c) and TE (d) waveguide modes. The black dash line indicates thelight line in air while the cyan dash line gives the light line in the SiO2 substrate.The solid lines are dispersion of waveguide modes in a reference flat planar air/a-Si/SiO2 waveguide with a-Si thickness of 175 nm, which are flipped into the Brillouinzone assuming a periodicity P =214 nm. The open circles are the leaky guided modedispersions of our grating-waveguide structure deduced by the resonant mode cal-culation tools of JCMsuite

planar layer response can be considered to be the background extinction re-sponse, though one must account that the grating structure would induce ashift to the broad Fabry-Perot features, which is more apparent for the TMcase. The peak extinction at the TM0 (720 nm) and TE0 (750 nm) resonantwavelengths is 1. Additionally, since the TM0 and TE0 resonances have rela-tively sharp linewidths, one can distinguish more easily that the contributionof the background extinction without the resonant is less than 0.1. This isa strong indication that our grating structure provides highly efficient cou-pling (>90% efficiency) between normal incident plane waves to the leakyguided modes (and by reciprocity from the leaky guided modes to the nor-mal outgoing plane wave). Resonant wavelength of TE1 waveguide mode isin a region where the background extinction is high. However, one can stillsee that the coupling is fairly strong as a distinct peak is still feasible. Theextinction at the TE1 resonant wavelength (640 nm) reaches 0.95 as comparedto the background extinction response around that wavelength range 0.725.

§3.3 PL and momentum space characterization 53

One thus see that at least 80 % of the power that would’ve otherwise be trans-mitted to the substrate without the grating structure is loss due to the TE1mode excitation. Thus, the coupling efficiency for the TE1 mode can alsobe expected to be in the range of 80%. Although one may be ignoring thesubtleties of interference effects that can be significant in cases with a strongbackground response, our conclusion of efficient coupling between radiationand waveguide modes is also supported by the fact that the leaky resonantexcitations is observed to cause distinct features in both the relative transmit-tance and extinction spectra. What’s more, A relation of the leaky waveguidemodes’ dispersion sustained by the grating-waveguide system at kx = 0 forG = 2π/214 nm is calculated in order to provide further clarity on the dis-persive nature of the modes. They are shown in Fig 3.3 for TM (c) and TE (d)modes, respectively.

3.3 PL and momentum space characterization

Figure 3.4: PL enhancement induced by the grating-waveguide structure. (a) Left: opticalimage of the sample. Right: 2D PL mapping of the sample. (b) PL spectrum of WSe2measured from on-grating and off-grating region. (c) Dependence of PL enhancementfactor on the excitation wavelength. (d) Time-resolved measurements from on-gratingand off-grating region, the pumping laser wavelength is 680 nm.

A monolayer of WSe2 exfoliated from a bulk crystal was dryly transferredonto the grating. Figure 3.4(a) shows the optical microscope (left) and 2D PL


mapping images (right) of the sample, respectively, where we could observeobvious PL enhancement induced by the grating. The micro-PL spatial map-ping were performed on a commercial WiTec alpha300S system in confocalmicroscope configuration, as shown in Fig.A.3. Here, we define the PL en-hancement factor (PLe f ) as the average on-grating PL intensity divided by theoff-grating value as shown in the formula under Fig. 3.4(a). By exciting thesample with a 633 nm (around the TE1 resonance) He-Ne continuous-wave(CW) laser, we observed up to 8 times enhancement of the PL from the on-grating area compared to the off-grating one. The spectra measured from twodifferent positions (on-grating and off-grating region) are shown in Fig. 3.4(b).

To confirm and distinguish the enhancement effects coming from excita-tion and emission, we also measured the dependence of the enhancementfactor on the excitation wavelength, as shown in Fig. 3.4(c). In these measure-ments, a Fianium WhiteLase supercontinuum laser was used as excitationsource, where 10 nm spectral band has been selected using an acousto-opticfilter, under the same average power as for data shown in Fig. 3.4(a). Thestrongest enhancement happens when the sample is excited by a laser wave-length of around 630 nm, which corresponds to the TE1 resonance of oursample and fulfills our expectation. The overall enhancement factor is slightlyweaker than that in our CW experiments, which is due to a broader spectraland pulsed (a few picoseconds) excitation. This experiment also shows thefeasibility of tuning the enhancement factor by varying the excitation wave-length.

In addition, time-resolved measurements were conducted to check theemission enhancement as shown in Fig. 3.4(d). For better comparison, here wenormalized the emission intensity to its respective maximum and plotted thedecay behavior in a logarithmic scale. We also fitted the decay curve into a bi-exponential function [197] shown as solid lines. We could observe that the ra-diative behavior of WSe2 for the on-grating region is around twice faster thanoff-grating one, which proves that we harvested emission enhancement fromour samples too due to the coupling of the monolayer WSe2 emission intothe leaky waveguide modes. Note that the decay curves are not straight lines(on a logarithmic scale), which is likely because there are multiple recombi-nation processes involved in the emission [197]. However, the detailed studyof the dynamics of carriers is beyond the scope of this work. Also, we foundthat the decay lifetimes of the delays were in the range of tens of picosec-onds, which offers the opportunity for ultrafast modulation with speed upto 50 Gbps. Thus, we conclude that our multi-resonant Si grating-waveguidestructure could effectively enhance PL of a WSe2 monolayer averagely up to8 times by combing both the excitation and emission enhancements.

To further explore the coupling between the monolayer WSe2 and grating-waveguide structure, we investigated the far-field angular emission from oursystem. Near- and far-field analyses are done using the finite element solverJCMsuite (JCMwave, Germany) [198]. In-plane momentum (kx, ky) distribu-

§3.3 PL and momentum space characterization 55

(b)

0 0.2 0.6 0.8 1.0

-0.5 0 0.5Kx/K0

-0.5

0

0.5Ky/K0

(d)

-0.5

0

0.5

Ky/K0

-0.5 0 0.5Kx/K0

(a)

(c)

0.4

Iref

I0 Iy

Ix

Figure 3.5: Experimental back-focal plane images of emission from monolayer WSe2. Anotch filter with half maximum bandwidth of 10 nm centered at 750 nm was usedto filter out the spectrum. (a) The overall emission from on-grating WSe2, (b, c) theback-focal plane images of the emission component polarized perpendicular (Iy) andparallel (Ix) to the grating ridge from the on-grating WSe2 structure, respectively. (d)Back-focal plane image of the total emission from off-grating WSe2 structure.

tion of the emission was obtained through back-focal plane imaging, whereeach point in the image plane maps to a specified angle of the emission [179].The in-plane momentum is related to the emission polar angle θ through therelation sin(θ) = k‖/k0, where k‖ =| kx + ky |, and k0 = 2π/λ is the wave vec-tor amplitude at wavelength λ. We observed quite different emission patternsfrom the on-grating and off-grating regions. Figure 3.5(a) shows the back-focal plane image of the total emission from the on-grating regions, wherewe observe that the emission goes preferentially into four distinct angular re-gions. In contrast, the back-focal plane image of emission from unpatternedregions, shown in Fig. 3.5(d), displays typical pattern with intensity decaying


from the center. Furthermore, we mapped the back-focal plane imaging of theemission of different polarizations. Figure 3.5(b) and 3.5(c) show the emissionpatterns when a polarizer oriented across and along the grating ridge was ap-plied in the detection path, respectively. These two images show clearly thatthe emission direction is polarization-dependent. Therefore, the emission di-rectionality and intensity in the grating region can be tailored with a polarizerto a great degree.

Figure 3.6: Experimental setup for PL characterization from monolayer WSe2. M1, M2,M3 and M4 are removable mirrors. We can switch between femtosecond and He-Ne633 nm lasers for excitation by removable mirror M1. Mirror M2 can switch betweenwhite light illumination and laser excitation, white light here is used to locate thesample. M3 can switch between CCD imaging and spectral measurements. M4 canswitch between integrated and time-resolved spectral measurements. L1, L2 , L3 andL4 are lens. L1 is in a removable mount, which could switch between real-space andback-focal-plane imaging. BS refers to beam splitter, Ob is objective. P1 is polarizerand λ/2 is half waveplate, which are used to tune the excitation polarization. P2is another polarizer that is used to distinguish different polarization components ofthe emission. Spectro refers to spectrometer. The streak camera is triggered by thefemtosecond laser.

All the PL spectral measurements and back-focal-plane imaging were con-ducted on an in-house microscopy system as shown in Fig 3.6 schemati-cally. A 100× objective with numerical aperture of 0.7 was used for exci-tation and collection of emission in reflection configuration. A 633 nm He-Necontinuous-wave was used as excitation source for integrated spectral andback-focal-plane imaging. A pair of lenses were used to translate the backfocal plane of the imaging objective to a CCD camera. An Optronis SC-10streak camera triggered by Coherent Chameleon Ultra II Femtosecond laserwith resolution down to 2 ps was used for time-resolved measurements, thesample is also excited by the Femtosecond laser at a central wavelength of680 nm, with a repetition rate of 80 MHz and a pulse duration of 140 fs.

§3.4 Numerical simulation 57

3.4 Numerical simulation

To investigate further the physical mechanism behind the measured PL char-acteristics, we performed numerical simulations of the emission of a WSe2monolayer coupled to the grating-waveguide structure. The WSe2 monolayeremission is modeled as a superposition of different electric dipole emitters,placed 1 nm above the grating, for three different lateral positions: in thecenter of the unit cell (this corresponds to the position above the center ofthe ridge), above the edge of the ridge (this corresponds to the position at58.5 nm from the center), and close to the boundary of the unit cell (corre-sponding to the position which is almost above the center of the trench). Asthe WSe2 monolayer does not support out-of-plane oriented dipole moments,[179] we only simulated in-plane oriented electrical dipoles, oriented across(y-direction) and along (x-direction) the grating ridge. Typically, simulating asingle dipole emission in a periodic system requires one to consider a largeamount of unit cells, which in full three dimensions is computationally timeconsuming. To handle this, we utilize a supercell algorithm which allowsus to deduce the singular dipole emission response in a periodic system bycombining single unit-cell simulations with varying phase relations along theperiodic boundaries [199].

For the far-field calculation of a singular dipole emission near the grating-waveguide structure, we utilized unit cells consisting of a 200 nm thick sub-strate of SiO2 and the a-Si grating with a 150 nm thick guiding layer and the50 nm thick ridge on top. Above the grating is air (refractive index n = 1). Asupper and lower boundaries of the unit cell, we place Perfectly Matched Lay-ers (PMLs) that attenuate the field to suppress reflections at the computationaldomain boundaries. The horizontal width of the unit cell is 214 nm and thewidth of the ridge is 107 nm. Periodic boundary conditions are used in the x-and y-direction. Each simulation of a unit cell with periodic boundary condi-tions implies that an infinite number of periodically arranged dipole sourceswith a certain phase relation between them are considered. By performinginverse Floquet transformation, which superpose the solutions for differentperiodic phase relations of the single unit cell results, we reconstruct the fieldof a singular dipole in a periodic system [199]. 128 supercells are used as acompromise between accuracy and computational time.

The simulated far-field distribution in momentum space, averaged overthe positions and orientations, is shown in Fig. 3.7(a). Good matching of thesingular dipole far-field calculations and the measured momentum space ofthe emission is obtained, when compared with Fig. 3.5(a). By consideringonly the far-field component perpendicular to the grating ridges [Fig. 3.7(b)],we reproduce the main features in Fig. 3.5(b), in which there is high peakintensity around ky ≈ ±0.3k0. Conversely, considering only the intensitycomponent parallel to the grating ridges [Fig. 3.7(c)], allows us to reproducethe features of Fig. 3.5(c).


Figure 3.7: Numerical simulation of the momentum space. Simulated momentum spacedistribution of the emission’s far-field averaged over the considered position andorientation. (a) Total far-field intensity. (b, c) Far-field intensity component perpen-dicular (Iy) and parallel (Ix) to the grating ridge, respectively . (d) Folded dispersionrelation of the TE0 and TM0 waveguide modes at a wavelength of 750 nm for a flatslab waveguide system assuming a period of 214 nm in the y-direction.

The observed polarization-selective directional emission property is linkedto the waveguide modes the emitters couple to. To demonstrate this, we cal-culated the dispersion relation of TE0 and TM0 waveguide modes for a flatslab waveguide system (air/ 175nm a-Si /SiO2) folded into the first Brillouinzone with a grating vector G = 2π/214 nm [Fig. 3.5(d)]. The folded k-spacecross-section of the waveguide mode dispersion leads to four curves relatedto ±1 diffraction coupling of radiation to the TE0 and TM0 waveguide modes.These four curves match well with what was observed in the experimentsand far-field simulations, which indicates that these are indeed the modes

§3.4 Numerical simulation 59

that the monolayer is coupling to. In addition to the folded dispersion curves,we show intensity plots obtained from 2D finite element simulations of a linedipole emission above the grating-waveguide and the flat multilayer structure[Fig. 3.8(a) and 3.8(b)]. As a-Si is not absorbing in the emission wavelength,the waveguide modes in the grating-waveguide region have a long propaga-tion range. Due to this, one would have to account for the contribution ofmany unit cells of the periodic system. Here, we show simulations assuming100 unit cells with the line dipole source placed in the center of the cen-tral unit cell. Figure 3.8(a) shows the intensity profiles when the dipole linesource is polarized along the grating ridges, which thereby excites TE waves.As can be seen in the intensity plots, a major portion of the emission couplesto the waveguide modes for both the case with and without grating. Efficientcoupling of the emission to the waveguide modes can also occur when thedipole line source is polarized along the y-direction, which excites TM waves[Fig. 3.8(b)]. Since efficient coupling of the emission to the waveguide modesoccurs, one can expect that the radiation properties would be dictated by thewaveguide modes’ radiative nature if their outcoupling is facilitated. Withoutthe grating structure, however, a large portion of the emission that couples tothe waveguide mode remains guided and does not affect the angular distri-bution of the detected PL signal.

Figure 3.8: Calculated intensity profiles. Calculated intensity profiles of singular linedipole emissions in a 2D system for multilayer structures with and without gratingsfor 100 unit cells, when the line dipoles are polarized parallel (a) and perpendicular(b) to the grating ridge, they are normalized to their respective maximum for bothcases. (i) and (ii) correspond to the on-grating and off-grating region, respectively.The line dipoles are placed 1 nm above the grating ridge (or the a-Si slab layer for theflat reference case). The line source is laterally placed at the middle of the center unitcell (middle of the ridge) in both case. (c) Angle-averaged intensity enhancement forthe grating case relative to flat case as a function of the excitation wavelength. Weconsider TE incoming polarization and assume the same Gaussian distribution of theincoming plane waves’ inclination angles as done for Fig. 3.2(d). The inset gives thetotal field profile for normal incidence at the peak resonant wavelength (640 nm).

Having discussed the origin of the polarization dependent directionality,we proceed to examine the photonic effects which provide enhancement at the


emission wavelength. We calculate the average ratio of total emitted powerby point dipoles in the grating-waveguide system relative to the flat case withthe expression Pgrat

tot /Pflattot , where Pgrat

tot indicates the total emitted power inthe grating structure and Pflat

tot the total emitted power of the flat structurewith a thickness of the a-Si layer of 200 nm. For the dipoles polarized acrossthe grating, we obtained a ratio of 1.5, which is comparable to the measuredlifetime enhancement indicating that the emission process is dominated byspontaneous emission and thus contributions of different dipoles to the PLcan be summed up in an incoherent manner. For the dipoles polarized alongthe grating, we only get a ratio of 1.01, which suggests that they have a longerlifetime in the grating system than the dipoles polarized across the grating.

To calculate the outcoupling enhancement, we compare the total dipoleemission power Ptot with the power radiated into air, Prad, both for the grat-ing structure and the flat structure. From our simulations, we get Pgrat

rad /Pgrattot

= 0.26 and Pflatrad/Pflat

tot = 0.11. This means that the portion of power outcoupledinto air in the grating system is by a factor of 0.26/0.11 = 2.36 larger thanin the flat system. Even when this outcoupling enhancement factor is mul-tiplied by the calculated life time enhancement factor (×1.5), the result doesnot match the PL enhancement factor obtained in the measurement. This en-hancement factor mismatch indicates that the grating structure does not onlyenhance the emission.

To further confirm the absorption enhancement of the pump light, whichcan contribute to the PL enhancement, we calculate the intensity enhance-ment 1 nm above the grating ridge for TE polarized light for different excita-tion wavelengths relative to a flat unpatterned multilayer slab. We considerplane waves incoming to the structure from air at different inclination an-gles as done in Fig. 3.2(d). The angle-averaged intensity enhancement for thewavelength range 500 nm to 700 nm is plotted in Fig. 3.8(c). An intensityenhancement peak around the wavelength of 640 nm is visible in agreementwith the measurement in Fig. 3.4(c). The intensity enhancement peak is dueto the excitation of a TE1 mode as shown by the inset figure, which shows thecalculated field intensity for normal incident plane wave. Our simulationsfurther show that one can obtain a peak intensity enhancement reaching 6times around 640 nm due to the TE1 mode excitation, which can be expecteddue to a also roughly 6 times maximum increase of absorption by the WSe2monolayer. Further engineering of the mode profile by the grating shape orthe placement of the emitter can potentially increase this even more.

3.5 Conclusion

We have demonstrated enhanced and polarization-selective directional emis-sion from monolayer WSe2 integrated onto a Si grating-waveguide structure.

§3.5 Conclusion 61

The PL enhancement and directionality have been realized by simultaneouslycoupling the emission and the excitation fields into the resonant modes sup-ported by the structure. By tailoring the resonant frequencies and dispersionof the waveguide modes, we have shown great flexibility in controlling theWSe2 monolayer emission in both intensity and directionality. Furthermore,our time-resolved measurements show that our structure could effectivelyreduce the lifetime of the radiation decay, which provides opportunities forultrafast modulation up to 50 Gbps. In addition, our numerical simulationshave revealed how different modes contribute to the emission enhancementand directionality, and the numerical results explain experimental data well.These findings, demonstrated on fully scalable Si-based platform, are impor-tant for chip-integrated optoelectronic applications of 2D materials.

Statement

This chapter is written based on the work in the journal paper:Chen, H.; Nanz, S.; Abass, A..; Yan J.; Gao, T.; Choi, D.-Y.; Kivshar, Y.S.;Rockstuhl, C.; Neshev, D. N. "Enhanced directional emission from monolayerWSe2 integrated onto a multi-resonant silicon-based photonic structure". ACSPhotonics, DOI:10.1021/acsphotonics.7b00550 (2017).

In this work, HC led the projects in idea conceiving, sample preparation,PL characterization, data analysis, paper writing. YJ contributed to the samplepreparation and PL characterization parts. The simulation was done with thehelp of SN, AA, CR. All other authors contributed to some part of the projectsand the discussion.

Chapter 4

Valley-based directional emissionfrom monolayer WSe2 mediated bynanoantenna

4.1 Introduction

As discussed in Sec. 1.3.2, the inversion symmetry breaking and quantumconfinement of the 2D TMDCs, especially in monolayer form, offer unprece-dented opportunities to explore valley-based physics and applications [36,43,112]. Valley pseudospin refers to degenerate energy extrema in momentumspace [36]. In 2D TMDCs, which have a hexagonal lattice structure, valleys ofdegenerate energy locate at the corners of the hexagonal Brillouin zone: theK and K’ points [26, 200]. Analogy to spintronics, valley pseudospin couldalso be potentially used as non-volatile information storage and processing,which is known as valleytronics [201–205]. Thus, it can be envisioned thatthe dynamic excitation and control of carriers in different valleys is crucial forfuture valley-based information technologies and applications.

In particular, monolayer TMDCs with direct bandgap at the K and K’points [35] makes it possible to control the valley freedom optically. Pump-ing of exciton of valley polarization have been demonstrated by polarization-resolved PL measurements [45–47]. And we reproduced the main features ofthese findings, Figure 4.1(a) shows the experimental setup used for polarization-resolved PL measurements, Figure 4.1(b) shows the optical images of themonolayer WSe2 sample we used in experiments (left) and schematic of thevalley selection rule of the emission (right). Figure 4.1(c) shows the polarization-resolved emission when the sample is excited by different circularly polarizedlaser, where we could observe that left- (right-) handed circularly componentdominates the emission when excitation is left (right) circularly polarized.

Based on these findings, valley-based light emitting diode with control-lable emission polarization [110], valley Hall effect [52], valley-dependentphotogalvanic effect have all been explored. Besides, excitonic valley coher-

63

64 Valley-based directional emission from monolayer WSe2 mediated by nanoantenna

Figure 4.1: Optical excitation of valley polarization. (a) Experimental setup built forcharacterizing the valley polarization from a monolayer WSe2. (b) Left: the opticalimage of the WSe2 sample exfoliated from bulk crystal used in experiments; mid-dle: schematic of the monolayer WSe2 and the first Brillouin zone structure; right:schematic of the valley-selection rules. (c) Polarization-resolved measurements of PLfrom a monolayer WSe2 under right/left circularly polarized light excitation.

.

ence [49], valley- and spin-polarized Landau levels [115] and valley Zeemaneffect [116–119] have all been studied in monolayer TMDCs too. Differentschemes have been developed, such as optical [120, 121], magnetic [104, 122]and electrical [49, 206], to control the valley pseudospin in 2D TMDCs, a fewexamples are shown in Fig. 4.2.

On the other hand, to facilitate device integration, it is preferable that

§4.1 Introduction 65

Figure 4.2: Control of valley polarization. (a) Circular polarization degree of excitonicPL from a monolayer WSe2 as a function applied magnetic field in Faraday geometry.Each line shows a different orientation of the magnetic field denoted by αB, whichis shown in part (ii). Part (iii) shows the inverse width 1/B1/2 as a function of thecos(αB), solid line is the linear fit [122]. (b) Degree of PL polarization as a functionof applied magnetic field for exciton (i) and trion (ii), respectively [104]. (c) Rotation-induced PL anisotropy S2 as a function of the excitation-control delay time τ, whichindicates that the intervalley decoherence time of a monolayer WSe2 is in the range ofhundreds of femtoseconds [120]. (d) Degree of PL polarization from a bilayer MoS2at 648 nm as a function of the gate voltage [206].

.

light emission from 2D TMDCs can be controlled at the nanoscale. Recentadvances in resonant metallic nanostructures, dubbed plasmonic nanoan-tennas, have shown such great capability and flexibility [30, 36, 112]. Plas-monic nanoantennas could significantly modify the emission of a localizedemitter at the nanoscale when the plasmonic modes in the antennas are ex-cited [164, 207, 208]. In particular, other than the fundamental dipole mode,localized emitters could effectively excite the higher-order modes in nanoan-


tennas that are in general weakly coupled (or uncoupled) to plane wave exci-tation [209,210]; the near-field and far-field interference of multiple plasmonicmodes offers nanoantennas unprecedented capability to control the emissionof localized emitters in various aspects [210–212]. Although previous stud-ies have shown designs for spin-dependent directional emission, their localresponse is still limited to linear polarization [212], and thus can not be em-ployed to control the emission of a localized emitter that emits circularly po-larized light .

Here, we propose a plasmonic nanoantenna-TMDC system that can effec-tively route light emission from different valleys of TMDCs into opposite di-rections. The nanoantenna can support electric dipole and electric quadrupoleresonances, and they can only be excited by localized dipole emitters with or-thogonal dipole moments. Due to the intrinsic π/2 phase difference betweenthe electric dipole and electric quadrupole emission, the scattering directionbecomes spin-locked when the nanoantenna is coupled to circular emitters.This valley-based scheme could provide useful insight for component designsuch as coupler and router for the future valley-based information processingsystem.

4.2 Antenna design principles

At resonances, the far-field radiation of nanoantenna could be expanded intomultipolar series, Equation 4.1 shows the first three terms, the electric dipolep, the electric quadrupole Q and the magnetic dipole m, in Cartesian coordi-nate system [213]

E(r) =k2

0eikdr

4πε0r

{[n× (p× n)] +

ikd6[n× (n× Qn)] +

1vd

(m× n)...}

(4.1)

where k0 and kd are the wave number in free space and medium respec-tively, vd is the light speed in medium, n is the unit vector in the direction ofemission, r is the coordinator vector, r = |r|.

From Eq. 4.1, we could see that the far-field radiation is in phase withelectric dipole moment, while there is a π/2 phase difference for electricquadrupole. Thus, there is naturally a π/2 phase difference between theelectric dipole and quadrupole emission when their corresponding chargesoscillate in phase, and the parallel components of electric dipole and electricquadrupole emission (strictly speaking, quadrupole is a tensor, while paral-lel is between two vectors) will interfere with each other depending on theirrelative phase and amplitude. When the amplitudes of the far-field compo-

§4.2 Antenna design principles 67

nent are comparable, the interference will be constructive in one direction anddestructive in the other direction when the phase difference between electricdipole and quadrupole is π/2 or 3π/2, while the interference is preventedif the phase difference is 0 or π. Our design is based on this interferenceproperty to tailor the emission directions from different valleys.

Figure 4.3: Design principles of the directional emission from different valleys. (a) Theproposed scheme to separate emission from different valleys through integratingwith properly designed nanoantennas, the directions of the emission from mono-layer TMDCs depend on the polarization sates of the excitation (different valleys areaddressed). (b) Principles of the interference between electric dipole and quadrupole,the direction of constructive interference depends on the relative phase difference be-tween the dipole and quadrupole.

.

The basic structure of our system is shown in Fig. 4.3(a), the emissionfrom different valleys is directed into defined directions by integrating the2D TMDCs layer onto well designed nanoantenna. When the system is ex-cited by light of different polarization states, the emission goes into differentdirections, thus offering us great freedom to control the emission from dis-tinct valleys, which could in potential act as information carrier. Here, we useinterference of multiple modes excited in the nanoantennas to realize suchfunctionalities. The general concept of how the nanoantenna works is shownin Fig. 4.3(b). Parallel electric dipole and quadrupole will interfere with eachother depending on their relative phase and amplitude, the interference willbe constructive in one direction and destructive in the other direction whentheir phase difference is π/2 or 3π/2, while the interference is prevented ifthe phase difference is 0 or π [214]. Thus, by changing the phase difference ofthe dipole and quadrupole from +π/2 to −π/2, we could tune the radiationdirection from one to the other effectively. On the other hand, emission fromTMDCs monolayer solely comes from the in-plane exciton or trion [179], andthe exciton could be generally treated as dipole emitter when interacting withphotonic structures [191]. So we use two in-plane dipole emitter to representemission from the 2D monolayer, +π/2 or −π/2 phase difference are appliedto mimic the left or right circularly polarized emission [215] from exciton indifferent valleys [216]. To demonstrate our idea clearly, we start with a simplenanoantenna design consisting of two bars.


4.3 Numerical calculation of two-bar antenna

Figure 4.4: Characteristics of the bar antenna excited by dipole emitter (a) (i) sideview of the simulation setup; (ii, iii) top view of the short bar and and longbar, respectively. The red arrows represents point dipole emitter with differentorientations. The red spots represent electric probes. (b, c) The electric fieldintensity and phase at the position of probe when dipole emitters with differentorientation are used as excitation source for short and long bar, respectively.We only show phase information for shortbar excited by horizontal emitter andlongbar excited by vertical emitter. The field intensity is normalized to largerone for emitters with different orientations. (d) Azimuthal polar plot of the total(P0) and azimuthal component (Pθ) of the far-field power distribution when theshortbar is excited by horizontal emitter. (e) Azimuthal polar plot of the total(P0) and azimuthal component (Pθ) of the far-field power distribution when thelongtbar is excited by vertical emitter. The direction of θ is illustrated by arrows.

.

Different plasmonic modes could be excited in a bar antenna when a lo-calized emitter is placed in the proximity of the bar, depending on a couple offactors such as the antenna size, emitter position and orientation. By choos-ing proper size parameters, either the dipole mode or the ‘dark’ quadrupolemode of the bar antenna could be excited dominantly by a local dipole source.We choose a short bar with length Lp=104 nm, width Wp=25 nm, and a long

§4.3 Numerical calculation of two-bar antenna 69

bar with length Lq=310 nm, width Wq=70 nm, the height of the two bars areboth 40 nm. The general side view of our simulation setup is shown in part(i) of Fig. 4.4, point dipole emitters are placed 5 nm above the antenna in Zdirection. To mimic the experimental practice, we simulate the antenna ontop of glass substrate. Two electric dipoles with horizontal (Dh) and vertical(Dv) orientation are placed 25 nm away from the bar antenna in Y direction.Electric probes are located at one end of the bar antennas to detect the elec-tric phase and amplitude. The setup for short bar and long bar antenna areshown in part (ii) and (iii) in Fig. 4.4, respectively.

We start by studying the individual response of the two bar antennas tolocal dipole emitter orientated along or across the bar by numerical calcu-lations using finite-integral frequency-domain simulations (CST MicrowaveStudio) with open boundary conditions. To avoid unphysical sharp edges,we model the antenna as rounded corners with a radius of curvature of 5 nm.The considered gold properties are based on experimental data from [177] forthe permittivity of gold in the visible/near-infrared spectral region.

The intensity of the electric field along X direction (I) and phase informa-tion (ϕ) at the probe position when the structure is excited by local dipoleemitters of different orientations, for short bar and long bar, are shown inFig. 4.4(b) and (c), respectively. For better comparison, we normalize the fieldintensity to the stronger one. As can be seen in Fig. 4.4(c), for the shortbar, the field induced by the horizontal dipole emitter (Ih) dominates at thewavelength range we are interested in. In contrast, the excited field from thevertical dipole emitter (Iv) dominates for the long bar. What’s more, both ofthe electric field intensity profiles show a resonant peak around 715 nm. Thephase information detected by the probes corresponds to the phases of theoscillating charges, which defines the phases of the dipole and quadrupolemoments. The phase information under the dominant excitation, labeled asϕh and ϕv are also shown in Fig. 4.4(b) and (c). We could observe that the tworesonant modes are in phase, thus the far-field radiation will have a phasedifference of π/2. To further investigate the nature of the excited modes inthe two antennas, we monitor the far-field radiation pattern of the horizon-tal emitter with short bar and vertical emitter with long bar at the resonantwavelength, which are shown in Fig. 4.4(e) and (f), respectively. Due to theexistence of the substrate, most of the emitted power goes into the high-indexmedium (lower half space). In the case of horizontal emitter with short bar an-tenna [Fig. 4.4(e)], the radiation pattern shows a typical dipole profile, whilethe emission shows quadrupole profiles for the case of vertical emitter withlong bar [Fig. 4.4(f)]. Besides, we show polar plot for both the total power(P0) and the azimuthal power component (power contributed from azimuthalelectric field, Pθ). As can be observed from both Fig. 4.4(e) and (f), the az-imuthal component (Pθ) dominates in both cases, which are expected for bothdipole and quadrupole radiation from bar antennas along the X direction.By examining the vectorial field profile in the near-field, we further confirmthat the electric dipole mode is excited dominantly by the horizontal emitter


when two dipole emitters are placed near the center of short bar, while theelectric quadrupole mode excited by the vertical emitter is dominant for thelong bar. Here we fine tune the geometries of the antennas in order to havethem resonate around 715 nm, since it matches our experimental results ofthe peak emission wavelength of the monolayer WSe2. The parameters of thetwo bars are further optimized such that the radiated far-field electric fieldshave comparable intensity.

Figure 4.5: Features of double-bar emission. (a) Schematic side and top view of thedouble-bar antenna. ∆ϕ represents the phase difference applied between the hori-zontal and vertical dipole emitter. ∆ϕ=±90o is used to mimic left or right circularlypolarized emitter, respectively. (b) Side view of far-field pattern when ∆ϕ=±90o isapplied. (c, d) Azimuthal polar plot of the total (P0) and azimuthal component (Pθ)of the far-field power distribution, respectively. We show both cases of ∆ϕ=±90o.

.

After investigating the response of the individual bar antennas, we per-form simulation for the combined system consisting of two bar antennasand local dipole emitters, the side and top views of the setup are shown inFig. 4.5(a). The gap between the two bars is set as 50 nm, and the dipole emit-ters are located in the center of the gap. To mimic the circular emitters, weimplement a phase shift between the horizontal and vertical dipole emittersdenoted as ∆ϕ, where ∆ϕ=±90o represents right or left circular emission fromthe emitters. The total radiation pattern (side view) are shown in Fig. 4.5(b)when ∆ϕ=90o or −90o are applied, respectively. Due to the interference ofthe fields from electric dipole and electric quadrupole, the original mirror

§4.3 Numerical calculation of two-bar antenna 71

symmetry of the radiation pattern breaks when a circular emitter presents.Importantly, the directionality could be tuned by changing the sign of thephase difference (circular polarization states) effectively. Figures 4.5(c) and(d) compare the polar plots of the total (P0) and azimuthal power compo-nent (Pθ) distribution, it is clear that the azimuthal power component stilldominates (the two figures are plotted in same unit), which confirms that thedirectional emission is mainly contributed by the interference between thedipole modes from short bar and the quadrupole mode from long bar. Toquantify the observed directionality, we define the front-to-back ratio (F/B)as ratio between the total power emitted in one half space to the other. Thevalue is 4.7 dB for the total radiation, and 6.0 dB for the azimuthal powercomponent, which could be distinguished by adding a polarizer in experi-ments. The directionality of the total radiation is slightly weaker than theazimuthal component because some other weaker modes are excited from thelong bar as well. Since the valley polarization of the emission from monolayerTMDCs depends on the polarization states of the pumping laser, we couldeasily tune the emission directionality from different valleys just by changingthe pumping polarization states in our TMDC-nanoantenna system.

Furthermore, we evaluate the emission enhancements brought by the plas-monic nanoantennas. The radiation enhancement is defined as the total powerradiated by the two dipole emitters coupled to antennas, normalized to thecase with no antennas. We find that the radiation is dramatically enhanced upto 15 times at the resonant wavelength. In addition, we check the robustnessof this design with regards to spectrum, and we find the directionality pre-serves from 680 nm to 750 nm. This broadband response makes it suitable tocontrol the emission from monolayer TMDCs such as WSe2 in whole emissionrange. Thus, the simple nanoantenna we propose here could effectively en-hance the emission intensity and tune the valley-based emission directionalityfrom TMDCs .

As discussed, the modes excited by the local dipole emitters depends onthe position of the emitters. To evaluate the average directionality offered byour proposed two-bar antenna, we perform scanning of position of the dipoleemitters, two cases are taken into account. Firstly, we investigate the averagedirectionality when the emitters are inside the gaps between the two bars bytaking 3 positions inside the gap as shown in Fig. 4.6(a). We simulate the casesof emitters at the 3 positions separately and then add up the radiation power,the polar plot of the total power and azimuthal power component are shownin Fig. 4.6(b) and (c), respectively. They show similar patterns as the case ofcentral position, while the front-to-back ratio decreases a bit after averagingdue to that the positions away from the center do not have directionality asgood as the center position. However, the average directionality still keeps 3.4dB for the total power and 4.2 dB for the azimuthal power component. Un-fortunately, after averaging over more positions outside the gaps [we take 9typical positions as shown in Fig. 4.6(d)], the directionality degrade a bit more,but we can still tune the emission direction by change the phase shift between


Figure 4.6: Average emission pattern. (a) Schematic of the 9 emitter positions usedto avaluate the average effects. (b, c) Azimuthal polar plot of the total (P0) andazimuthal component (Pθ) of the far-field power distribution after averaging over allthe positions.

.

the two emitters (equivalently changing the excitation polarization states forthe TMDCs). However, with the development of materials fabrication tech-niques, nanostructure of TMDCs [217–219] could be fabricated efficiently, sowe can control the position and size of the TMDCs. Thus, a system consistingof the bar antenna and TMDCs nanosheet only inside the gap between thebars could in principle serve as efficient light source with tunable emissiondirection.

4.4 Discussion and conclusion

To further understand our system and seek for ways to improve the averagedirectionality. We compare the total radiation power by the emitters acrossdifferent positions as shown in Fig. 4.6(d). The central position, where weobserve best directionality, emits 2 to 5 times stronger than other positions.The average directionality could be better if the central position had a muchstronger emission power. Indeed, directional emission from local emitters en-

§4.4 Discussion and conclusion 73

abled by plasmonic nanoantennas is highly sensitive to the position of theemitters [210, 214]. To improve the directionality, we do need structures withvery strong ’hot’ spots and the emission shows good directionality when theemitters are located at the spots. This might direct us to further improveour structures by introducing antenna shape like bowtie [220] or split-ring-resonators [214]. However, such structures have more geometric parametersand more complicated modes when excited by local emitters, the process tofind the optimized geometric size are difficult and time consuming. More-over, more complicated structures requires demanding fabrication efforts inpractice. In contrast, the bar antenna we propose has simple mode profilesand easy to optimize the size, and the fabrication process is relatively straight-forward.

In conclusion, we proposed a paradigm to control the emission intensityand direction from valleys in monolayer TMDCs using multimode plasmonicantennas. We designed a nanoantenna based on two gold bars, of which thedipole and quadrupole modes can be excited dominantly at the same fre-quency. The interference between the dipole and quadrupole modes resultsin directional emission, and the direction depends on the phase difference be-tween these two modes. By mimicking the circular emission from valleys inTMDCs with circular dipole emitters, we have shown that the emission (leftcircular or right circular) from different valleys can be directed into oppositedirections when the emitters couple to the two-bar nanoantenna, with a direc-tionality of up to 6 dB, and a radiation power enhancement of up to 15 times.In addition, we discussed the reasons for the degrading directionality whenaveraging over different positions and proposed the methods to address thisissue either by structuring the materials or by designing new structures. Thenanoantenna we proposed here could be potentially useful in future valley-based devices, such as imaging and light information processing.

Statement

This chapter is written based on the work in the journal paper:Chen, H.; Liu, M.; Xu, L.; Neshev, D. N. "Valley-selective directional emis-sion from a monolayer transition metal dichilcogenide mediated by plasmonicnanoantennas". To be submitted to Beilstein Journal of Nanotechnology (In-vited, 2017).

In this work, HC led the projects and did all the simulation work, ML, LXand DNN contributed to the discussion.

Chapter 5

Enhanced Second-harmonicGeneration (SHG) from 2D WSe2 inguided-wave geometry

5.1 Introduction

Monolayer TMDCs exhibit advanced optoelectronic properties as discussedin above sections, which include, but are not limited to direct bandgap, ro-bust valley polarization and strong electric tunability. These properties haveopened opportunities for a number of applications, including ‘flat-land’ emit-ters [35, 165, 221] and valley-based applications [46, 47, 49]. Especially, non-linear optical wavelength conversion of two-dimensional (2D) TMDCs andin particular SHG has attracted lots of attention [124, 125, 134–136, 136, 222–224], as these 2D materials are intrinsically non-centrosymmetric. Extraordi-nary strong SHG has been reported for various materials such as monolayerWSe2 [225] and MoS2 [124, 134, 226]. In Section 1.3.3, we also introducedhow SHG from 2D TMDCs could be tuned by pumping [58] and electri-cal gating [114], and how it could be used as useful tools for determiningthe the crystal properties and orientation [125, 132–134]. However, the sub-nanometer monolayer thickness of such monolayer materials limits the lengthof their nonlinear interaction with light, and thus the overall conversion effi-ciency. Thin gold film substrate [227][Fig. 5.1(a)], optomechanical cavity [223][Fig. 5.1 (b)], microcavity [228] [Fig. 5.1(c)] and photonic crystal cavity [229][Fig. 5.1(d)] have been demonstrated to enhance the SHG from MoS2 lay-ers [227]. But, in all experiments to date, the 2D materials are excited alongthe normal of the monolayer, hence the overall nonlinear conversion efficiencyis still limited by the sub-nanometer nonlinear interaction length with light,thus preventing their future practical application. Besides, these approachesare either not compatible with the widely used silicon-based platform or re-quire complex fabrication and positioning skills.

On the other hand, silicon photonics plays a crucial role in modern pho-tonic technologies, including a number of nonlinear applications for frequency

75

76Enhanced Second-harmonic Generation (SHG) from 2D WSe2 in guided-wave geometry

Figure 5.1: SHG enhancement from 2D TMDCs by photonic integration. (a) SH signalfrom a monolayer MoS2 on SiO2/Si substrate and 17nm MoS2 layer from Au/SiO2substrate, the upper inset shows the sample images and the lower inset shows the Ra-man spectrum of single-layer MoS2 on SiO2/Si substrate [227]. (b) Schematic imageof the optomechanical platform with double resonance used to enhance SHG froma monolayer MoS2 (left) and the SHG from on- and off-cavity regions (right) [223].(c) Schematic representation of the microcavity designed to enhance SHG from 2DMoS2 [228]. (d) Illustration of structure of how the photonic crystal cavity is used toenhance the SHG from a monolayer MoS2 [229].

.

conversion and signal processing. However the centrosymmetric propertiesof silicon inhibit any second order (or χ(2)) nonlinear effects, such as SHG,thus limiting the range of possible applications [230–232]. Various hybridintegration approaches for incorporating non-centrosymmetric materials inthe silicon photonics platform have been suggested [188] in order to achievesecond order nonlinearity [231], however with very limited success. The 2DTMDCs can likely provide a viable solution for integration within the siliconphotonics platform due to their strong Van der Waals interactions to surfaces.Furthermore, due to their ultrathin nature the integration with Si waveguideswill not be disturbing the waveguide modes [233] or hindering other func-tionalities. However, the integration of 2D TMDCs with Si waveguides andthe demonstration of second order nonlinear effects, such as SHG, has notbeen demonstrated to date.

Here, we develop a monolayer MoSe2 Si-waveguide integrated, scalableplatform for second order nonlinear effects in silicon photonics and experi-mentally demonstrate strong SHG enhancement in comparison to free-space

§5.2 Waveguide design and sample fabrication 77

SHG from TMDCs. Importantly, our experiments show that the nonlinearinteraction length with light for 2D TMDCs could be dramatically increasedthrough integration with waveguides, and even achieve exact phase matchingof χ(2) parametric processes in a silicon photonics platform. Our results pavethe way for practical χ(2) nonlinear applications in silicon, including efficientwavelength conversion, parametric amplification and generation of entangledphotons.

5.2 Waveguide design and sample fabrication

Figure 5.2: Linear characterization. (a) Schematic design of the hybrid integration ofMoSe2 onto a Si-waveguide.(b) top: Schematic side view of the grating coupler forboth in- and out-coupling, where the numbers mark the physical dimensions in nm;bottom: SEM top view of the two grating couplers. (c) Optical image of the samplebefore transferring MoSe2 monolayer (left), PL mapping of the sample after MoSe2transferring (right), the bright area corresponds to the MoSe2 monolayer. (d) PLspectrum of the monolayer MoSe2 at room temperature, measured on the blue spotin panel (c). In (c) and (d) the PL is excited by a cw 532 nm laser.

The concept behind the integration of MoSe2 on a Si waveguide is illus-trated in Fig. 5.2(a) (side view). A grating inscribed onto the waveguide isused to couple light from free space into the waveguide. The evanescent fieldof the waveguide mode at the fundamental frequency (FF) at ∼ 1550 nm over-laps with the MoSe2 material on top of the waveguide to generate secondharmonic (SH) wave. The generated SH can be guided and extracted out ofthe waveguide into free space by another grating coupler. Importantly, thisscheme can also promote other χ(2) nonlinear processes, including parametric


amplification and spontaneous parametric down conversion (SPDC).

Slab waveguide was used in our experiments because it allows us to testthe SHG at different propagation directions with respect to the TMDCs crys-talline orientation. Compared to crystalline silicon whose absorption start toincrease sharply below 1100 nm, hydrogenated amorphous silicon is transpar-ent up to 700 nm owing to high optical bandgap of 1.73 eV [196]. Hence theamorphous silicon was chosen in this work because of its low optical loss atboth spectral regions around 1550 nm (FF) and 775 nm (SH). The thicknessof 220 nm was chosen because it was commonly used in silicon photonicsplatform [234, 235]. Furthermore, the TE0 mode of the FF exhibits relativelystrong evanescent field on the surface of the waveguide. In experiments, a220 nm layer of hydrogenated amorphous silicon was deposited on SiO2/Siwafer by plasma enhanced vapor deposition at 300 ◦C. The refractive indexand extinction coefficient of the material was measured by ellipsometry meth-ods afterwards.

To design the grating couplers for the FF and the SH fields, we computethe effective refractive indices of TE0 FF mode and TE1 SH mode. For sim-plicity, we use a conventional binary grating design, as schematically shownin Fig. 5.2(b) (upper part). A scanning electron microscopy (SEM) of the topview of the grating is shown in Fig. 5.2(b) (lower part) as well. In general,the coupling efficiency of the grating depends on a number of parameters,including the incident beam profile, incident angle, grating geometry, gratingperiod, duty cycle and etching depth [131]. In our work, but without lossof generality, we implemented a grating with 50% duty cycle and a periodwhich enables the in/out-coupling at normal incidence for the first diffractionorder [131]. We experimentally tested a set of etching depths and achievedcoupling efficiency of about 16%, which is reasonably good for our purposeand comparable to other couplers reported in literature [236, 237]. In order toenable multiple angles of excitation with respect to the MoSe2 crystal as wellas to achieve optimal coupling into the waveguide, we use a circular geom-etry for the grating coupler [238], where one half of the grating is designedfor in-coupling of light at a wavelength of 1550 nm, while the other half out-couples light at 775 nm. The grating structure was patterned by electron beamlithography at 20 kV using the positive resist ZEP-520A. The development wasperformed by inserting the sample into n-Amyl acetate. The resulting resistpattern was used as an etch mask for amorphous silicon etching in CHF3/SF6plasma. The residual resist was removed by oxygen plasma. Details of thefabrication are shown in Fig. A.1. The optical image of the top view of thegrating is shown in Fig. 5.2(c)(left).

Next, a monolayer of MoSe2 is exfoliated from a bulk crystal and drilytransferred onto the planar waveguide area inside the circular grating. Be-cause the optical contrast between the monolayer and the amorphous siliconis relatively poor, we used PL mapping instead of optical microscopy to locatethe MoSe2 position. Figure 5.2(c) (right) shows the 2D PL mapping image of

§5.3 SHG characterization 79

the sample: the monolayer MoSe2 crystal is the bright piece inside the gratingcircle. To confirm that the transferred piece is indeed a monolayer, we mea-sured its PL emission spectrum. Figure 5.2(d) shows the PL spectrum fromthe location marked with a blue dot, as indicated in panel c. The spectral peakis around 1.6 eV, which agrees well with literature reports [167, 176, 193]. Themicro-PL spectroscopy and micro-PL spatial mapping were performed on acommercial WiTec alpha300S system in confocal microscope configuration asshown in Fig. A.3, using excitation by 532 nm CW laser.

5.3 SHG characterization

Figure 5.3: Experimental setup for SHG characterization. Polarizer P1 and half waveplateλ/2 are used to tune the polarization of the excitation. Polarizer P2 is used to measuredifferent components of the signal. λ/2 and P2 are mounted in automatic rotationalstage so that we could measure the co-polarized component distribution. M1, M2 andM3 are removable mirrors. M1 switches between white light illumination and laserexcitation, white light is used to locate the sample. M2 switches between infraredcamera and CCD imaging. The infrared camera is used to locate the laser spot. M3switches between spectral measurements and CCD imaging. Lens L1, L2 and L3 areused to condense light. DM refers to dichroic mirror, which transmits in the infraredrange and reflects in the visible. Ob is objective. F is a bandpass filter. Spectro refersto spectrometer.

In the next step, we study the SHG from the MoSe2 monolayer. For SHGmeasurements, a FemtoFiber Pro femtosecond laser of central wavelength1550 nm, repetition rate of 80 MHz and pulse duration of 82 fs was used topump the sample. An in-house setup was built for these measurements,the setup is shown in Fig. 5.3. Unless otherwise specified, average powerof 20 mW was used. An in-house microscopy system with 20× objective wasused for excitation and collection. The focused laser spot size was 5µm, thepeak power density was around 15 GW/cm2. In the polarization resolvedmeasurements, a half waveplate was used to rotate the incident light polar-ization and another polarizer was used for detection. As discussed previ-ously, the process of SHG is strongly enhanced by resonant pumping, near


Figure 5.4: Nonlinear SHG microscopy. (a) Emission spectra measured from the sam-ple when focusing the pump-laser on the grating (red) and on the MoSe2 (blue), thefocusing positions are shown as red and blue spots in Fig. 5.2(c), respectively. (b andc) Power dependence (in log-log scale) of the peaks R1 (b) and R2 (c) as indicatedin panel a. The values are normalized to the quantities obtained at 2.9 mW of FFpower. The dots are the measured data and the line shows the expected quadraticdependence. (d) The polar intensity distribution of the emission component polar-ized parallel to the FF polarization, when rotating the pump polarization, ϕ, by 360◦

for both SH signal (asterisk and dashed red fitting line) and 2P-PL (black dots), the30◦-210◦ direction corresponds to the armchair axis of the monolayer MoSe2, shownschematically in the right-hand side.

the two-photon transition [58]. This justifies our material choice of MoSe2,which exciton transition is resonantly matched to the two-photon energy ofour pump-laser (around 0.8 eV). Under excitation by the focused FF beam,we observe strong exciton emission at 1.6 eV. The grating size in the radialdirection of our sample is 10 µm and the focused laser spot is roughly 4 µm,hence we could choose to focus the laser spot either directly on the monolayerMoSe2 or on the grating area. Figure 5.4(a) shows the spectra (normalized tomaximum value) collected from the sample when exciting the MoSe2 crys-tal directly from free space [blue spot in Fig. 5.2(c)] and from the waveguidethrough the grating coupler [red spot in Fig. 5.2(c)]. Here the spectral signalonly comes from the monolayer MoSe2, as we did not observe any measur-able signal from waveguide region without MoSe2 using a separate referencesample. Importantly, we observed approximately 5 times enhancement ofthe emission signal at 1.6 eV, when exciting the monolayer by the evanescentwaveguide mode, as compared to excitation from free space.

We found that the signal intensity does not depend on the laser polariza-

§5.3 SHG characterization 81

tion when focusing on the MoSe2 directly from free space. However, whenfocusing on the grating, the signal intensity is heavily dependent on laser po-larization, as expected for the properties of our grating coupler. The spectraldata shown here has been taken by optimizing the polarization for the redspot, which corresponds to position with nearly maximum interaction lengthin our system.

Because the pump-laser is in resonance with the exciton energy, the SHemission and two-photon luminescence (2P-PL) are nearly degenerate. How-ever, we still observe two peaks when focusing the laser on MoSe2 directly[R1 and R2 in Fig. 5.4(a)]. There is also a broad tail in the emission spectrumwhen focusing on the grating. This is likely caused by the fact that the laserwe used in experiments is relatively broadband (from 0.79 eV to 0.81 eV, ).While the signal–R1 dominates the emission, we find that both peaks scalequadratically with excitation power, as shown in Fig. 5.4(b) and (c), respec-tively. To further distinguish them, we measured how the different emissioncomponents depend on the polarization of the pump-laser coupled from freespace. Figure 5.4(d) shows the polar distribution of the emission intensityparallel to the incident laser polarization (co-polarized component) as a func-tion of the polarization of the excitation laser. We observe a six-fold patternfor the main peak R1 (asterisk and red dashed line), which is expected forSH signal in a monolayer TMDCs [124,125,132–134] and reflects the 3-fold ro-tational symmetry of the crystal. From these SH microscopy measurements,we can also determine the crystalline orientation of the monolayer MoSe2.This is schematically depicted on the right-hand side of Fig. 5.4(d). In con-trast, the intensity of co-polarized component of peak R2, shown as blackdots in Fig. 5.4(d), does not depend on the pump-laser polarization. Thesepolarization measurements confirm that the resonant peak R1 is indeed theSH signal, while other peaks with much weaker intensity are 2P-PL. In thefollowing discussion, we will focus only on the SH signal.

As mentioned above, the grating coupler is sensitive to the incident laserpolarization and works best for TE0 mode coupling, namely, when the laseris polarized along the azimuthal direction of the circular grating. The caseof 2D material on top of a waveguide under TE0 excitation was first studiedtheoretically by Haus and Reider some forty years ago [239] and recent predic-tions [184] have shown that such geometry can lead to strong SHG enhance-ment. However no experimental testing of these ideas have been attemptedto date. Here, we measure the SH signal as a result of such interaction. Todemonstrate this in details, two typical points P1 and P2 have been excited onthe grating, as shown in Fig. 5.5(a) (left). The coordinate system is the sameas in Fig. 5.4(d). P2 is on the armchair axis and P1 is at an angle of around30◦ to it. Figure 5.5(a) (right) shows the positions of P1 and P2 relative tothe coordinate system and MoSe2 orientation. Firstly, we measure the overallSH intensity dependence on the polarization of the pump-laser over 360◦, asshown in Fig. 5.5(b) (i, ii) for P1 and P2, respectively. The coordinates systemis the same as in panel a and the angle corresponds to the polarization of the


Figure 5.5: SHG from MoSe2 loaded Si waveguide. (a) Map of the sample orientationrelative to the polar coordinate system for the measured sample (left) and schematicview (right), the armchair of the MoSe2 is around 30◦ to the horizontal axis. Thetwo spots P1 and P2 are the different positions of the laser focus on the grating,when exciting the waveguide mode. (b) Total SH emission intensity dependence onthe pump-laser polarization, when focusing on position P1 (i) and P2 (ii), respec-tively. Co-polarized SH intensity dependence on pump-laser polarization for P1 (iii)and P2 (iv), respectively. All the intensities are normalized to the maximum value;the blue asterisks are the measured data and the dashed red lines are best fits; theangle refers to the polarization direction of the pump-laser. (c) Microscope imagesof the SH emission when pumping from P1 and P2, respectively, demonstrating thewaveguiding and out-coupling of the SH signal.

pump-laser. We could see from these two images that both dependencies dis-play a figure-of-eight shape distribution. This shape is entirely defined by thecoupling characteristic of the grating, since the in-coupling is efficient onlyfor one polarization.

However, the polarization dependence changes when we measure the SHemission co-polarized to the pump-laser, when varying laser polarization.The results are shown in Fig. 5.5(b) (iii, iv) for P1 and P2 excitation, respec-tively. We observed different profiles for these two positions, which is likelydue to the combined effects from the grating coupler and the 3-fold rotationalsymmetry of the monolayer MoSe2. Furthermore, we took snapshots of theemission when pumping at these two points as shown in Fig. 5.5(c). Bandpassfilters have been applied to make sure that the signal captured by camera isdominated by the SH signal. We could see that SH signal is generated at theposition of the MoSe2 monolayer and is guided into the waveguide, beingsubsequently coupled out from the grating on the left. We note that someemission also comes back from the input end and some signal is scattered outdirectly from the material into free space. Importantly, the out-coupling sig-nal was stronger when pumping from P1 compared with P2. Based on theseresults, we could see some hints that phase matching between TE0 mode forpumping and TE1 mode for SHG plays a role here, however they also indicatethat multiple nonlinear wave-mixing processes exist in our system.

§5.4 Theoretical calculation 83

5.4 Theoretical calculation

Figure 5.6: Numerical simulations. (a) Effective mode indices as a function of thecore thickness for the TE- and TM-polarized guided modes at the fundamental fre-quency (FF) and second harmonic (SH). The three red circles indicate the closestphase matching points. (b) Color scale representation of the SH conversion efficiency(on a logarithmic scale) provided by the waveguide for the three dominant three-wave-mixing processes, i.e., TE0 → TE1 (red solid box), TE0 →TM0 (blue dashedbox) and TE0 →TM1 (green dashed box); the radial coordinate is the waveguidelength (from 0 to 30 µm) and the azimuthal coordinate is the angle between theguided-modes propagation direction and the horizontal axis. The light-blue dottedcircles refers to a waveguide length of 22 µm, approximately equal to the sample size.Purple and green dots correspond to the points P1 and P2 of the experiment, respec-tively. (c) Total (solid red lines) and co-polarized (dashed red lines) SH intensities asfunctions of the pump-laser polarization angle, ϕ (measured with respect to x-axis)when focusing on positions P1 (purple dots) and P2 (green dots).

To support our experimental results and explore further direction to op-timize our system, we performed simulations based on coupled-mode the-ory [240]. The intensity of the SH signal depends on several factors, namely:the overlap integral between the FF and SH guided modes, the phase match-ing between these modes, the crystal orientation defined by the guided-modes


wavevector and the armchair direction of the MoSe2 crystal, the efficiency ofthe input grating for the pump-laser beam and the efficiency of the outputgrating in the extraction of SH light. In Fig. 5.6(a) we plot the effective modeindex as a function of the waveguide thickness for the guided modes involvedin SHG, assuming 1550 nm as the pump-laser wavelength.

The waveguide supports three phase matching points for SHG [red circlesin Fig. 5.6(a)], involving three different combinations of guided modes at theFF and SH frequencies. The silicon core thickness (220 nm) is close to two ofthese points: one is associated with the TE0 → TE1 SHG process while theother is related to the TM0 → TM1 process. Our simulations suggest thatthe structure of the input grating, which mainly couples FF light into the TE0guided mode, favors the TE0 → TE1 interaction. In addition to this process,the nonlinear monolayer allows two other interactions originated from theFF TE0 mode, i.e., the TE0 → TM0 and the TE0 → TM1. This shows theflexibility of our hybrid-integration scheme for selecting different parametricinteractions, including other three-wave mixing process such us parametricamplification and generation, as well as SPDC.

The internal conversion efficiency provided by the waveguide for the dom-inant nonlinear interaction, TE0 → TE1, is given by

ηTE0→TE1 = PSH/P2FF = ξ2

NLL2wg

sin2 (∆βLwg/2)(

∆βLwg/2)2 (5.1)

where PFF is the power per unit length of the FF TE0 mode at the waveguideinput, PSH is the SH power per unit length in the TE1 mode measured atthe waveguide output, Lwg is the interaction length along the waveguide,∆β = 2βFF − βSH is the wavevector mismatch. The nonlinear overlap factorin Equation (5.1) is defined as

ξNL = χsMoSe2

sin (3ϑ)

(8π2

ε0cλ2FFnSHn2

FF

)1/2(

E∗(TE1)SH E2(TE0)

FF

)∣∣∣z=z2D(∫

wg

∣∣∣E(TE0)FF

∣∣∣2dz)(∫

wg

∣∣∣E(TE1)SH

∣∣∣2dz)1/2

(5.2)where χs

MoSe2= 5.85× 10−18 m2/V, similar to other 2D crystals (WS2) [225],

is the quadratic nonlinear susceptibility of MoSe2, ϑ is the angle formed bythe guided-modes wavevector and the armchair direction of the MoSe2 crys-tal, λFF = 1550 nm is the pump wavelength, nFF,SH are the effective refractiveindices of the FF and SH modes, EFF is the FF TE0 mode profile and ESH isthe SH TE1 mode profile. In addition, z2D indicates the vertical position ofthe MoSe2 surface, i.e., the interface between the silicon film and the air su-perstrate. The two normalization integrals at the denominator are calculatedalong the vertical direction (z axis). The expressions of the efficiency and thenonlinear overlap factor for the TE0 → TM0 and the TE0 → TM1 interactionscan be written in a form analogous to Equations (5.1) and (5.2) by considering

§5.4 Theoretical calculation 85

the appropriate effective refractive indices and mode profiles, and replacingsin(3ϑ) with cos(3ϑ) in order to properly take into account the 2D crystalanisotropy.

In Fig. 5.6(b) we show the calculated conversion efficiency for the threeSHG processes discussed above as a function of the interaction length Lwg(varying from 0 to 30 µm) and the angle between the guided-modes wavevector and the horizontal axis. The color maps are on a logarithmic scale. Themost coherent and efficient process is the TE0 → TE1 interaction, whose max-imum efficiency is about two orders of magnitudes larger than the efficiencyof the other two processes. Due to the crystal anisotropy, when the FF TE0guided mode is excited near the point P1 (purple dots, corresponding to aninteraction length of about 22 µm and ϑ = 30◦), the SHG is dominated by theTE0 → TE1 interaction and the other two interactions involving TM modes atthe SH frequency are vanishing. On the other hand, when the TE0 FF guidedmode is excited near the point P2 of the sample (green dots, correspondingto an interaction length of about 22µm and ϑ = 0), the opposite response isobtained, i.e., the TE0 → TE1 interaction is significantly suppressed whereasTE0 → TM0 and TE0 → TM1 interactions are maximized.

Next, we estimate the SH light intensity at the output grating as a functionof the pump beam polarization angle, ϕ and compare these theoretical resultsto our experimental findings. The total SH intensity extracted by the outputgrating

ITOT(ϕ) ∝1

∆ϑ∆λ

∫∫∆ϑ,∆λ

[KTE1ηTE0→TE1(ϑ, λFF)

]sin2(ϕ + Θ)dϑdλ

+1

∆ϑ∆λ

∫∫∆ϑ,∆λ

[KTM0ηTE0→TM0(ϑ, λFF) + KTM1ηTE0→TM1(ϑ, λFF)

]sin2(ϕ + Θ)dϑdλ

(5.3)and the portion of the SH light co-polarized with the pump laser polarization,

ICP(ϕ) ∝1

∆ϑ∆λ

∫∫∆ϑ,∆λ

KTE1ηTE0→TE1(ϑ, λFF)sin2(ϕ + Θ)sin2(ϕ + Θ− ϑs)dϑdλ

+1

∆ϑ∆λ

∫∫∆ϑ,∆λ

[cos2(ϕ + Θ)KTM0ηTE0→TM0(ϑ, λFF)

]sin2(ϕ + Θ− ϑs)dϑdλ

+1

∆ϑ∆λ

∫∫∆ϑ,∆λ

[cos2(ϕ + Θ)KTM1ηTE0→TM1(ϑ, λFF)

]sin2(ϕ + Θ− ϑs)dϑdλ

(5.4)are proportional to the internal conversion efficiencies provided by the waveg-uide for each SHG interaction (η terms) and to the coupling efficiencies of the


output grating for each SH guided mode (K terms). ϑ is the angle formed bythe guided-modes wavevector and the armchair direction of the MoSe2 crys-tal. The angle Θ = ϑ− ϑc, where ϑc = 30◦, indicates the azimuthal positionof the sample spot illuminated by the pump laser. Given its circular shape, weassume that when the input grating is illuminated by the pump laser beam,it creates a small cone of propagating guided TE0 modes that originates frompoints P1 and P2 with angular divergence ∆ϑ = 3◦. In other words, Θ variesfrom -1.5◦ to +1.5◦ for point P1, whereas for point P2 Θ varies from 26.5◦

to +29.5◦. The double integrals in Equations 5.3 and 5.4 represent averagesacross the angular range ∆ϑ and across a range of wavelengths ∆λ = 15 nmthat corresponds to the pump laser bandwidth centered around the centralwavelength (1550 nm). The extraction efficiencies of the output grating for thethree SH guided modes, corresponding to the coefficients K in Equations 5.3and 5.4, have been numerically retrieved with a finite-element solver (COM-SOL): in particular we find that KTM1 = 4KTE1 and that KTM0 = 4.48KTE1 .Moreover, we assume that the angular shift ϑs between the output polarizer,which is used to filter co-polarized SH light, and the input polarizer be equalto 4◦.

The estimated total and co-polarized SH light intensities versus pump-laser polarization angle are reported in the polar plots of Fig. 5.6(c) for thetwo illumination positions investigated experimentally. The good agreementbetween theory and experiment, revealed by comparing Fig. 5.6(c) and Fig-ures 5.5b, corroborates the idea that the waveguide is indeed boosting theSHG of the nonlinear monolayer via the three nonlinear interactions men-tioned above.

Finally, we have calculated the possible maximal possible yield of SHGthat the MoSe2-loaded silicon waveguide configuration could achieve un-der perfect phase-matching conditions. For example, the optimization of theTE0 → TE1 process can be obtained via complete phase matching by chang-ing the waveguide core thickness to 236 nm. Under the pumping conditionsof the experiment-spot size with a diameter of around 5 µm - and assumingdiffraction-free propagation of the guided modes in the lateral (non-confined)dimension, a 22 µm long waveguide would provide a SH signal 280-timesstronger with respect to the case of direct pumping of the monolayer fromthe top at normal incidence, i.e. in the absence of guided modes. This SHenhancement can be explained as follows: on one hand, the waveguide con-figuration amplifies the nonlinear interaction length by a factor Lwg/tMoSe2 ,where tMoSe2 = 0.65 nm is the monolayer thickness; on the other hand, theoverlap integral is limited by the very small thickness of the nonlinear ma-terial. It is worth stressing that, at phase matching, the enhancement factorwould scale up quadratically with the nonlinear interaction length: for exam-ple, a 1-mm-long waveguide would boost the enhancement factor from 280 to5.8x105.

§5.5 Conclusion 87

5.5 Conclusion

In conclusion, we have demonstrated the integration of TMDC monolayer ona silicon photonic platform for quadratic nonlinear optics applications. Inparticular, we demonstrate 5 times enhancement of SHG from atomically thinmonolayer MoSe2 by excitation of the 2D material by the evanescent field ofthe guided mode of a 220 nm planar waveguide. This enhancement is dueto the increased interaction length, which proves that the nonlinear interac-tion length with light of 2D TMDCs, limited by monolayer thickness could beovercome by integration with waveguide. Moreover, our calculations revealhow the mode conversion works in our system in different situations and theresults match well our experiments. The developed modeling predicts thatthe nonlinear signal could be further enhanced by optimizing the waveguidethickness to enable full phase matching condition. The results pave the wayfor many other nonlinear applications of 2D materials in optical domain, in-cluding parametric oscillations or efficient generation of entangled photonsources by SPDC. All such applications can be further advanced by possibleelectrical control of the nonlinear interactions in TMDCs [114].

Statement

This chapter is written based on the work published in the journal paper:Chen, H.; Corboliou, V.; Solntsev, A. S.; Choi, D.-Y.; Vincenti, M.A ; Ceglia,D.d.; Angelis, C.D.; Lu, Y.; Neshev, D. N. "Enhanced second harmonic gener-ation from two-dimensional MoSe2 on a silicon waveguide". Light. Sci. Appl.6, e17060 (2017).

In this work, HC led the projects in sample preparation, SHG characteriza-tion, data analysis, paper writing. The simulation was done with the help ofMAV, DdC, CDA. All other authors contributed to some part of the projectsand the discussion.

Chapter 6

Conclusion and outlook

6.1 Conclusion

The renaissance of 2D materials including TMDCs has brought countless newopportunities in the ’flatland’, in both fundamental and applied physics. Inparticular, the monolayer TMDCs with direct bandgap have versatile light-emitting properties including strong PL, single-photon emission, valley po-larization and SHG, which makes them potentially serve for multi-functionallight source in future optoelectronics. What’s more, the layered TMDCs areheld together by out-of-plane van-der-Waals forces and can be transferredonto a silicon substrate without lattice-mismatch issues, which makes themsuitable candidates to integrate into silicon photonics platforms.

However, challenges remain for the practical applications of monolayerTMDCs. Due to the subnanometer thickness nature of these materials, thelight emission efficiency is much lower compared to other III-IV direct bandgapmaterials. Besides, other emission properties of 2D TMDCs such as direction-ality need to be well controlled for certain applications. Coupling to photonicnanostructures is promising to boost the light-emitting efficiency for these 2Dmaterials, since photonic nanostructures have great advantages in controllinglight-matter interaction at nanoscale. In this thesis, we explore integration ofmonolayer TMDCs into different photonic platform including metallic plas-monic and non-metallic silicon structures, and demonstrate flexible control ofthe emission from monolayer TMDCs, which paves the way for many appli-cations for these 2D materials. Here is a brief summary of the work we havedone.

We demonstrate integration of monolayer MoSe2 onto plasmonic antennaconsisting of gold bars. The plasmonic resonance is designed to overlap withPL peak from monolayer MoSe2. We realize PL manipulation from strongenhancement to quenching by changing the spacer thickness between the an-tenna and monolayer MoSe2 experimentally, and we also show control of theemission polarization to some extend. Furthermore, we investigate the cou-pling mechanism between the plasmonic antenna and the monolayer MoSe2

89

90 Conclusion and outlook

numerically. We find that the overall quantum efficiency of the system is themain factor that affects the PL harvesting, which depends heavily on the dis-tance between plasmonic antenna and the emitting layer. Thus, we learn thatit is crucial to control the distance between the antenna and the monolayerMoSe2 carefully to best harvest the PL emission. By the time we publishedour work, it was the first time that a plasmonic-MoSe2 was studied. Im-portantly, we found the crucial factor that affects the coupling between theplasmonic antenna and the monolayer MoSe2, which clarifies some conflictsshown in previous studies. This work paves the way for understanding thecoupling between monolayer TMDCs and plasmonic platforms, thus for re-lated applications.

We demonstrate the integration of monolayer WSe2 onto silicon-basedgrating-waveguide scheme and realize enhanced and directional emissionfrom monolayer WSe2. By aligning the resonant modes supported by thegrating-waveguide structure with both the excitation and emission wavelength,we realize average PL enhancement up to 8 times through combining bothexcitation and emission enhancement. What’s more, the dispersion of themodes routes the emission into defined directions, which is also polariza-tion dependent. Thus, we realize enhanced and directional emission frommonolayer WSe2 by integrating with silicon-based photonic structure. In ad-dition, we demonstrate that this grating-waveguide structure could effectivelyreduce the radiative lifetime of the emission from monolayer WSe2, whichoffers the feasibility for ultrafast signal processing. Though plasmonic plat-form shows great advantages in confining energy at nanometer scale and thuscould boost light-matter interaction dramatically, while the enhancement re-lies on local ’hot’ spots. Besides, the metallic structure is not suitable forthe modern silicon-photonics platform and requires precise positioning skills.In contrast, the scheme we demonstrate here is fully scalable and suitablefor silicon photonics applications. This work opens the door to implementatomic-scale, multi-functional, flexible and efficient light source onto siliconphotonics platform.

We propose a TMDCs-nanoantenna system that could effectively enhanceand separate emission from different valleys in monolayer TMDCs into dis-tinct directions. By mimicking the emission from valleys in monolayer WSe2(TMDCs) as circular dipole emitters, we demonstrate that the emission fromdifferent valleys goes into opposite directions when coupling to the two-barplasmonic nanoantenna. The directionality derives from the interference be-tween the dipole and quadrupole modes excited in the two bars, respec-tively. Since the emission from valleys in 2D TMDCs could be addressedby optical excitation, we could tune the emission direction from the TMDCs-nanoantenna system by tuning the pumping without changing the antennastructure. Furthermore, we discuss the general principle and further direc-tions to improve the average performance of the nanoantenna structure. Theinversion symmetry breaking and strong spin-orbit coupling in 2D TMDCsbring exciting opportunities for studying valleytronics. Especially, the emis-

§6.2 Outlook 91

sion from different valleys in monolayer TMDCs could be addressed optically,which opens new door for valley-based applications. The scheme we pro-posed here could potentially serve for important component for valley-basedapplications such as non-volatile information storage and processing.

We demonstrate enhanced SHG from monolayer MoSe2 by integrationwith silicon waveguide. Instead of excitation from free space, we excitethe monolayer MoSe2 by guided modes supported by the waveguide. Thisscheme allows for phase matching and dramatically increases the nonlinearinteraction length between the excitation light and the materials comparedto free-space excitation, thus boost the second-harmonic signal. The inver-sion symmetry breaking in monolayer TMDCs brings new opportunities fornonlinear optics especially for SHG, while the efficiency is low due to thesub-nanometer thickness of these materials preventing them from practicalapplications. The scheme we demonstrate here show that the limited light-matter interaction length could be overcome by waveguide integration, thusopening lots of new opportunities for applications of these 2D TMDCs. Inparticular, these monolayer TMDCs are suitable for integration with silicon-photonics platform without lattice-mismatch issues, the structure we demon-strate here could serve for second-harmonic source in silicon chip, while sili-con itself does not own second-order nonlinearity due to the symmetric struc-ture. Furthermore, theoretical calculation reveals the coupling and conversionmechanisms in our system, and points out further directions for optimization.The fully scalable platform we demonstrate here brings new opportunities forthese 2D TMDCs especially for nonlinear chip-integrated applications.

6.2 Outlook

The field of 2D materials is developing rapidly, so does the new designs ofphotonic nanostructures. The work we demonstrate in this thesis could beextended to directions of both fundamental and applied physics, and thereare plenty of exciting opportunities ahead.

More understanding of coupling between photonic nanostructures and2D materials is needed to better control the properties of these materials.Many novel materials are emerging, for example, layered WTe2 (one memberof TMDCs) have been reported to possess large and non-saturating magne-toresistance [241]. Besides, new 2D materials such as boron nitride [183],phorsphore [242], and silicene [243] have also been studied. On the otherhand, novel photonic nanostructures especially dielectric ones [187, 244] withmultiple types of resonances have brought unprecedented opportunities tostudy the coupling between the photonic structures and 2D materials. Forexample, it will be interesting to investigate how the resonant magnetic-typenanostructures affect the magnetoresistance properties of WTe2. What’s more,heterostructure formed by stacking different kinds of TMDCs [81, 101, 102]

92 Conclusion and outlook

or mixing with other 2D materials [83, 245, 246] have shown advanced elec-tronic and optical properties, integration of these heterostructure with pho-tonic nanostructures will further control and enhance their performance. Forexample, it will be intriguing to see how resonant photonic structure affectsthe charge transfer between different materials across the layers. What’s more,the properties of 2D materials could be tuned by electric or magnetic field, itwill be interesting to investigate the tunability for hybrid structures consistingof 2D materials and photonic nanostructures. In particular, polariton modesformed through coupling between the TMDCs and cavities (strong coupling)has shown lots of interesting physical phenomena recently [247–250], therewill be plenty of room to explore here.

Integration of photonic structures with devices consisting of 2D materi-als. Optoelectronic devices consisting of 2D materials such as photodetec-tors, transistors and modulators have shown excellent performance. Theperformances could be further improved by incorporating proper photonicnanostructures, for example, previous work has shown that the sensitivityof the photodetectors could be improved by incorporating plasmonic struc-tures [251–255]. In addition, as we discussed, 2D TMDCs could be servefor versatile light source for future optoelectronic applications, integration ofphotonic structures could effectively increase the emission efficiency and thedirectionality. Recent work has demonstrated enhanced single-photon emis-sion from 2D materials by integration with nanostructures [256, 257] . Onthe other hand, nanostructured 2D materials themselves might be used to im-prove the performance of devices too [184,258], we could potentially constructhybrid system consisting of photonic structure and structured nanomaterialswith the developing of materials fabrication techniques.

With the study of basic properties of various 2D materials and devicesbuilt from them, Feynman’s dream has come true. Integration of 2D materialwith photonic nanostructures plays an important role and drives the dreamfurther. Looking ahead, integration of various 2D circuit elements such asTMDCs show potential to create ultra-compact, low-power, flexible electronicdevices, which will revolutionize optoelectronics.

Appendix A

Appendix

A.1 Fabrication procedures for a-Si grating

In Chapter 3 and 5, the grating are fabricated by electron beam lithography(EBL) followed by inductively coupled plasma (ICP) etching. The key step-to-step procedures are shown in Fig.A.1. In Chapter 5, the amorphous siliconlayer was deposited onto a SiO2/Si wafer, in the diagram of procedures, weomit the Si handle wafer. The detailed fabrication steps are laid out as below:

Figure A.1: The key step-to-step fabrication procedures for a-Si grating. The depostionthickness of the a-Si differs for different applications.

.

1. Depositing amorphous silicon (a-Si) onto glass by plasma-enhancedchemical vapor deposition (PECVD) using Oxford Instrument. The gases floware 475 sccm Helium and 25 sccm Silane at 250 degree Celsius, chamber pres-sure is 1500 mTorr, the forward power is 15 W.

2. Cleaning the a-Si surface with oxygen plasma (1 min, 200 W). Spin-coating a thin layer of HMDS (hexamethyldisilazane) as an adhesion promoter(3000 rpm, 30 s) followed by a layer of diluted positive photoresist ZEP520A(6000 rpm, 2 min). Then the sample is baked for 3 mins at 180 0C. Here wedo not show the layer of HMDS in the diagram.

93

94 Appendix

3. Just before loading sample for EBL, a thin layer of e-spacer is coatedby spin coating for conduction purpose. The grating is then patterned byelectron-beam exposure (20 kV, 10 µm aperture).

4. After exposure, the e-spacer is washed away by drilled water, then colddevelopment is performed by inserting the sample into Zep developer for80 s followed by rinsing sample with isopropanol. The resulting photoresistpatterns act as etching mask.

5. Inductively coupled plasma (ICP) etching process (15 mTorr chamberpressure, 15 W RF power, 400 W induction power) using CHF3 (50 sccm) andHF6 (1.8 sccm) as etch gases is conducted for form the desired structures.The etching depth is controlled via in-situ optical monitoring. The remainingphotoresist is removed by oxygen plasma.

Please note that parameters such as the time duration and temperature foreach process vary slightly depending on the resist and developer used for aparticular sample. The numbers given here provide a rough indication of thetime scale and temperature range for each process.

A.2 Transmittance characterization setup

All the transmittance data of the samples presented in this thesis are mea-sured from the pre-existing setup shown in Fig.A.2. A halogen bulb is usedas light source, whose brightness could be adjust by changing the voltage.Lens L1 with short focal length near the light source, followed by an open irisalong the light path. A polarizer P1 in the light path is used to choose thepolarization of incident light when linearly polarized beam is needed, whichcould be removed when not needed. Objective (Ob1) with a almost closed irisare used to focus light onto the sample, the iris restricts the angles of light in-cident into the objective (on the sample). Another objective (Ob2) in confocalconfiguration with Ob1 is used to collect the transmitted light. The sampleis mounted onto a 3D translational stage, so we could locate our sample atthe focal plane of the objectives. Light coming out of Ob2 then goes througha pair of lens (L2 and L3), between which there is an rectangular knife edge.The knife edge is used to choose the desired sample area. A removable mirrorindicated as dashed line after L3 is used to switch between spectral measure-ments and imaging samples. when the mirror is presented in the light path,the sample is imaged on the camera through lens L4, so we could choosethe desired sample region through moving the knife edge. The transmittedlight is directed onto the spectrometer through an objective Ob3 (for focusingpurpose).

All the lenses and distances between optical components are chosen suchthat the samples are illuminated with near-normal incident plane waves and

§A.3 PL mapping setup 95

that a focused image can be obtained at the CCD camera. The objectives Ob1and Ob2 were 20x Mitutoyo Plan Apo NIR infinity-corrected objectives withnumerical apertures NA= 0.4 and focal lengths f = 200 mm. The objective Ob3was a 10x objective of the same NA. The range of incident angles was reducedto ±3oC by the iris before Ob1.

All the transmittance measured from this system are obtained by referringto the transmitted light in the unpatterned area in our samples.

Figure A.2: Schematic of the setup for transmittance measurements. A halogen illuminatessystem as light source.L1, L2, L3 and L4 are lens with 1 inch diameter of carefullychosen focal lengths. Ob1, Ob2 and Ob3 are objectives used as light condenser. Prepresents polarizer. The solid black lines mean irises. The dashed line is a removablemirror. Spectro here refers to spectrometer.

.

A.3 PL mapping setup

The photoluminescence (PL) mapping of the samples shown in this thesiswere measured by a commercial WiTec-alpha300S system in confocal micro-scope configuration, the setup of this system is shown in Figure A.3. The ex-citation light source are coupled into the system through fibers and we couldchange excitation source depending on requirements. This system could berun in both reflection and transmission mode (we show transmission here).The PL scanning is enabled by the piezo scanner and the avalanche photodiode (APD) is used to detect the signal. In addition, the spectrometer alsoenable us to measure the spectral data.

96 Appendix

Figure A.3: Setup for PL mapping. The tunable light source supports wavelengths inwide range from 500 nm to 900 nm. The filters could also be changed to fit withdifferent purposes.

.

References

1. P. R. Wallace, “The band theory of graphite,” Phys. Rev., vol. 71, no. 9,p. 622, 1947. (cited on page 2)

2. J. McClure, “Diamagnetism of graphite,” Phys. Rev., vol. 104, no. 3, p. 666,1956. (cited on page 2)

3. J. Slonczewski and P. Weiss, “Band structure of graphite,” Phys. Rev.,vol. 109, no. 2, p. 272, 1958. (cited on page 2)

4. G. W. Semenoff, “Condensed-matter simulation of a three-dimensionalanomaly,” Phys. Rev. Lett., vol. 53, no. 26, p. 2449, 1984. (cited on page 2)

5. E. Fradkin, “Critical behavior of disordered degenerate semiconductors.II. spectrum and transport properties in mean-field theory,” Phys. Rev. B,vol. 33, no. 5, p. 3263, 1986. (cited on page 2)

6. F. D. M. Haldane, “Model for a quantum Hall effect without Landaulevels: condensed-matter realization of the" parity anomaly",” Phys. Rev.Lett., vol. 61, no. 18, p. 2015, 1988. (cited on page 2)

7. R. Peierls, “Quelques propriétés typiques des corps solides,” in Annalesde l’institut Henri Poincaré, vol. 5, pp. 177–222, 1935. (cited on pages 2and 10)

8. L. D. Landau, “Zur theorie der phasenumwandlungen II,” Phys. Z. Sow-jetunion, vol. 11, pp. 26–35, 1937. (cited on page 2)

9. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atom-ically thin carbon films,” Science, vol. 306, no. 5696, pp. 666–669, 2004.(cited on pages 2 and 3)

10. K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grig-orieva, S. Dubonos, and A. Firsov, “Two-dimensional gas of masslessdirac fermions in graphene,” Nature, vol. 438, no. 7065, pp. 197–200, 2005.(cited on page 2)

11. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observa-tion of the quantum hall effect and berry’s phase in graphene,” Nature,vol. 438, no. 7065, pp. 201–204, 2005. (cited on page 2)

12. K. Novoselov, “Nobel lecture: graphene: materials in the flatland,” Rev.Mod. Phys., vol. 83, no. 3, p. 837, 2011. (cited on page 3)

97

98 References

13. K. F. Mak, M. Y. Sfeir, J. A. Misewich, and T. F. Heinz, “The evolutionof electronic structure in few-layer graphene revealed by optical spec-troscopy,” Proc. Natl. Acad. Sci. U.S.A., vol. 107, no. 34, pp. 14999–15004,2010. (cited on page 3)

14. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth,T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant definesvisual transparency of graphene,” Science, vol. 320, no. 5881, pp. 1308–1308, 2008. (cited on page 3)

15. C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elas-tic properties and intrinsic strength of monolayer graphene,” Science,vol. 321, no. 5887, pp. 385–388, 2008. (cited on page 3)

16. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao,and C. N. Lau, “Superior thermal conductivity of single-layer graphene,”Nano Lett., vol. 8, no. 3, pp. 902–907, 2008. (cited on page 3)

17. A. S. Mayorov, R. V. Gorbachev, S. V. Morozov, L. Britnell, R. Jalil, L. A.Ponomarenko, P. Blake, K. S. Novoselov, K. Watanabe, T. Taniguchi, et al.,“Micrometer-scale ballistic transport in encapsulated graphene at roomtemperature,” Nano Lett., vol. 11, no. 6, pp. 2396–2399, 2011. (cited onpage 3)

18. J. Moser, A. Barreiro, and A. Bachtold, “Current-induced cleaning ofgraphene,” Appl. Phys. Lett., vol. 91, no. 16, p. 163513, 2007. (cited onpage 3)

19. J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. Van Der Zande, J. M. Parpia,H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranesfrom graphene sheets,” Nano Lett., vol. 8, no. 8, pp. 2458–2462, 2008.(cited on page 3)

20. A. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim,“The electronic properties of graphene,” Rev. Mod. Phys., vol. 81, no. 1,p. 109, 2009. (cited on pages 2 and 4)

21. A. K. Geim, “Graphene: status and prospects,” Science, vol. 324, no. 5934,pp. 1530–1534, 2009. (cited on pages 2 and 4)

22. K. S. Novoselov, V. Fal, L. Colombo, P. Gellert, M. Schwab, K. Kim, et al.,“A roadmap for graphene,” Nature, vol. 490, no. 7419, pp. 192–200, 2012.(cited on page 4)

23. B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Wiley, 2007.(cited on pages 5 and 7)

24. A. M. Fox, Optical Properties of Solids. New York: Oxford University Press,2001. (cited on page 6)

25. C. Kittel, Introduction to Solid State Physics 8th Edition. New York: JohnWiley and Sons Ltd, 2004. (cited on page 8)

References 99

26. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valleyphysics in monolayers of MoS2 and other group-VI dichalcogenides,”Phys. Rev. Lett., vol. 108, no. 19, p. 196802, 2012. (cited on pages 8, 12,13, 18, 20, and 63)

27. J. Wilson and A. Yoffe, “The transition metal dichalcogenides discussionand interpretation of the observed optical, electrical and structural prop-erties,” Adv. Phys., vol. 18, no. 73, pp. 193–335, 1969. (cited on page9)

28. A. Yoffe, “Layer compounds,” Annu. Rev. Mater. Sci., vol. 3, no. 1, pp. 147–170, 1973. (cited on page 9)

29. A. D. Yoffe, “Low-dimensional systems: quantum size effects and elec-tronic properties of semiconductor microcrystallites (zero-dimensionalsystems) and some quasi-two-dimensional systems,” Adv. Phys., vol. 42,no. 2, pp. 173–262, 1993. (cited on page 9)

30. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S.Strano, “Electronics and optoelectronics of two-dimensional transitionmetal dichalcogenides,” Nat. Nanotechnol., vol. 7, no. 11, pp. 699–712,2012. (cited on pages 10, 11, 15, 23, 29, 47, and 65)

31. B. Radisavljevic, A. Radenovic, J. Brivio, i. V. Giacometti, and A. Kis,“Single-layer MoS2 transistors,” Nat. Nanotechnol., vol. 6, no. 3, pp. 147–150, 2011. (cited on pages 11 and 12)

32. Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, and W. Tang, “First principlesstudy of structural, vibrational and electronic properties of graphene-likeMX2 (M=Mo, Nb, W, Ta; X= S, Se, Te) monolayers,” Physica B: CondensedMatter, vol. 406, no. 11, pp. 2254–2260, 2011. (cited on page 11)

33. A. Kuc, N. Zibouche, and T. Heine, “Influence of quantum confinementon the electronic structure of the transition metal sulfide TS2,” Phys. Rev.B, vol. 83, no. 24, p. 245213, 2011. (cited on pages 10 and 11)

34. M. Y. Han, B. Özyilmaz, Y. Zhang, and P. Kim, “Energy band-gap en-gineering of graphene nanoribbons,” Phys. Rev. Lett., vol. 98, no. 20,p. 206805, 2007. (cited on page 10)

35. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thinMoS2: a new direct-gap semiconductor,” Phys. Rev. Lett., vol. 105, no. 13,p. 136805, 2010. (cited on pages 10, 12, 13, 15, 16, 22, 29, 42, 63, and 75)

36. K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semicon-ductor transition metal dichalcogenides,” Nat. Photonics, vol. 10, no. 4,pp. 216–226, 2016. (cited on pages 10, 12, 13, 15, 18, 19, 22, 23, 29, 47, 48,63, and 65)

37. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, andF. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett.,vol. 10, no. 4, pp. 1271–1275, 2010. (cited on pages 10, 12, 13, and 15)

100 References

38. T. Li and G. Galli, “Electronic properties of MoS2 nanoparticles,” J. Phys.Chem. C, vol. 111, no. 44, pp. 16192–16196, 2007. (cited on page 10)

39. S. Lebegue and O. Eriksson, “Electronic structure of two-dimensionalcrystals from ab-initio theory,” Phys. Rev. B, vol. 79, no. 11, p. 115409,2009. (cited on page 10)

40. F. Schwierz, “Graphene transistors,” Nat. Nanotechnol., vol. 5, no. 7,pp. 487–496, 2010. (cited on page 10)

41. R. Fivaz and E. Mooser, “Mobility of charge carriers in semiconductinglayer structures,” Phys. Rev., vol. 163, no. 3, p. 743, 1967. (cited on page10)

42. V. Podzorov, M. Gershenson, C. Kloc, R. Zeis, and E. Bucher, “High-mobility field-effect transistors based on transition metal dichalco-genides,” Appl. Phys. Lett., vol. 84, no. 17, pp. 3301–3303, 2004. (citedon page 10)

43. X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layeredtransition metal dichalcogenides,” Nat. Phys., vol. 10, no. 5, pp. 343–350,2014. (cited on pages 12, 13, 18, 20, 29, and 63)

44. Z. Zhu, Y. Cheng, and U. Schwingenschlögl, “Giant spin-orbit-inducedspin splitting in two-dimensional transition-metal dichalcogenide semi-conductors,” Physical Review B, vol. 84, no. 15, p. 153402, 2011. (cited onpage 12)

45. T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang,B. Liu, et al., “Valley-selective circular dichroism of monolayer molybde-num disulphide,” Nat. Commun., vol. 3, p. 887, 2012. (cited on pages 12and 63)

46. K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarizationin monolayer MoS2 by optical helicity,” Nat. Nanotechnol., vol. 7, no. 8,pp. 494–498, 2012. (cited on pages 12, 20, 47, 63, and 75)

47. H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization inMoS2 monolayers by optical pumping,” Nat. Nanotechnol., vol. 7, no. 8,pp. 490–493, 2012. (cited on pages 12, 19, 20, 47, 63, and 75)

48. G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan,T. Amand, B. Liu, et al., “Robust optical emission polarization in MoS2monolayers through selective valley excitation,” Phys. Rev. B, vol. 86,no. 8, p. 081301, 2012. (cited on pages 12 and 47)

49. A. M. Jones, H. Yu, N. J. Ghimire, S. Wu, G. Aivazian, J. S. Ross, B. Zhao,J. Yan, D. G. Mandrus, D. Xiao, et al., “Optical generation of excitonicvalley coherence in monolayer WSe2,” Nat. Nanotechnol., vol. 8, no. 9,pp. 634–638, 2013. (cited on pages 12, 20, 47, 64, and 75)

References 101

50. D. Xiao, M.-C. Chang, and Q. Niu, “Berry phase effects on electronicproperties,” Rev. Mod. Phys., vol. 82, no. 3, p. 1959, 2010. (cited on page12)

51. Y. D. Lensky, J. C. Song, P. Samutpraphoot, and L. S. Levitov, “Topolog-ical valley currents in gapped dirac materials,” Phys. Rev. Lett., vol. 114,no. 25, p. 256601, 2015. (cited on page 12)

52. K. F. Mak, K. L. McGill, J. Park, and P. L. McEuen, “The valley hall effectin MoS2 transistors,” Science, vol. 344, no. 6191, pp. 1489–1492, 2014.(cited on pages 12, 13, 19, 20, and 63)

53. K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F. Heinz, and J. Shan,“Tightly bound trions in monolayer MoS2,” Nat. Mater., vol. 12, no. 3,pp. 207–211, 2013. (cited on pages 12 and 13)

54. J. S. Ross, S. Wu, H. Yu, N. J. Ghimire, A. M. Jones, G. Aivazian, J. Yan,D. G. Mandrus, D. Xiao, W. Yao, and X. Xu, “Electrical control of neu-tral and charged excitons in a monolayer semiconductor,” Nat. Commun.,vol. 4, p. 1474, 02 2013. (cited on pages 12, 13, 15, and 16)

55. Z. Ye, T. Cao, K. O’Brien, H. Zhu, X. Yin, Y. Wang, S. G. Louie, andX. Zhang, “Probing excitonic dark states in single-layer tungsten disul-phide,” Nature, vol. 513, no. 7517, pp. 214–218, 2014. (cited on pages 12and 13)

56. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan,D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding en-ergy and nonhydrogenic rydberg series in monolayer WS2,” Phys. Rev.Lett., vol. 113, no. 7, p. 076802, 2014. (cited on pages 12 and 13)

57. K. He, N. Kumar, L. Zhao, Z. Wang, K. F. Mak, H. Zhao, and J. Shan,“Tightly bound excitons in monolayer WSe2,” Phys. Rev. Lett., vol. 113,no. 2, p. 026803, 2014. (cited on pages 12 and 13)

58. G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal,A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe2 monolayers by laser excitation at excitonresonances,” Phys. Rev. Lett., vol. 114, no. 9, p. 097403, 2015. (cited onpages 12, 13, 20, 21, 22, 47, 75, and 80)

59. T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, “Theory ofneutral and charged excitons in monolayer transition metal dichalco-genides,” Phys. Rev. B, vol. 88, no. 4, p. 045318, 2013. (cited on pages 12and 13)

60. D. Y. Qiu, H. Felipe, and S. G. Louie, “Optical spectrum of MoS2: many-body effects and diversity of exciton states,” Phys. Rev. Lett., vol. 111,no. 21, p. 216805, 2013. (cited on pages 12 and 13)

61. Y. Zhang, T.-R. Chang, B. Zhou, Y.-T. Cui, H. Yan, Z. Liu, F. Schmitt,J. Lee, R. Moore, Y. Chen, H. Lin, H.-t. Jeng, S.-K. Mo, Z. Hussain, A. Ban-sil, and Z.-X. Shen, “Direct observation of the transition from indirect to

102 References

direct bandgap in atomically thin epitaxial MoSe2,” Nat. Nanotechnol.,vol. 9, no. 2, pp. 111–115, 2014. (cited on page 12)

62. M. M. Ugeda, A. J. Bradley, S.-F. Shi, H. Felipe, Y. Zhang, D. Y. Qiu,W. Ruan, S.-K. Mo, Z. Hussain, Z.-X. Shen, et al., “Giant bandgap renor-malization and excitonic effects in a monolayer transition metal dichalco-genide semiconductor,” Nat. Mater., vol. 13, no. 12, pp. 1091–1095, 2014.(cited on page 12)

63. G.-B. Liu, W.-Y. Shan, Y. Yao, W. Yao, and D. Xiao, “Three-band tight-binding model for monolayers of group-VIB transition metal dichalco-genides,” Phys. Rev. B, vol. 88, no. 8, p. 085433, 2013. (cited on page12)

64. P. Cudazzo, I. V. Tokatly, and A. Rubio, “Dielectric screening in two-dimensional insulators: implications for excitonic and impurity states ingraphane,” Phys. Rev. B, vol. 84, no. 8, p. 085406, 2011. (cited on page13)

65. A. Ramasubramaniam, “Large excitonic effects in monolayers of molyb-denum and tungsten dichalcogenides,” Phys. Rev. B, vol. 86, no. 11,p. 115409, 2012. (cited on page 13)

66. H.-P. Komsa and A. V. Krasheninnikov, “Effects of confinement and envi-ronment on the electronic structure and exciton binding energy of MoS2from first principles,” Phys. Rev. B, vol. 86, no. 24, p. 241201, 2012. (citedon page 13)

67. H. Haug and S. W. Koch, Quantum theory of the optical and electronic prop-erties of semiconductors. World Scientific Publishing Co Inc, 2009. (citedon page 13)

68. J. Feldmann, G. Peter, E. Göbel, P. Dawson, K. Moore, C. Foxon, andR. Elliott, “Linewidth dependence of radiative exciton lifetimes in quan-tum wells,” Phys. Rev. Lett., vol. 60, no. 3, p. 243, 1988. (cited on page13)

69. H. Haug and L. Bányai, Optical switching in low-dimensional systems.Springer, 1989. (cited on page 13)

70. J. Shang, X. Shen, C. Cong, N. Peimyoo, B. Cao, M. Eginligil, and T. Yu,“Observation of excitonic fine structure in a 2D transition-metal dichalco-genide semiconductor,” ACS Nano, vol. 9, no. 1, pp. 647–655, 2015. (citedon page 13)

71. Y. You, X.-X. Zhang, T. C. Berkelbach, M. S. Hybertsen, D. R. Reichman,and T. F. Heinz, “Observation of biexcitons in monolayer WSe2,” Nat.Phys., vol. 11, no. 6, pp. 477–481, 2015. (cited on page 13)

72. S. Schmitt-Rink, D. Chemla, and D. Miller, “Linear and nonlinear opticalproperties of semiconductor quantum wells,” Adv. Phys., vol. 38, no. 2,pp. 89–188, 1989. (cited on page 13)

References 103

73. M. Fogler, L. Butov, and K. Novoselov, “High-temperature superfluiditywith indirect excitons in van der Waals heterostructures,” Nat. Commun.,vol. 5, 2014. (cited on page 13)

74. M. Koperski, K. Nogajewski, A. Arora, V. Cherkez, P. Mallet, J.-Y.Veuillen, J. Marcus, P. Kossacki, and M. Potemski, “Single photon emit-ters in exfoliated WSe2 structures,” Nat. Nanotechnol., vol. 10, no. 6,pp. 503–506, 2015. (cited on pages 13, 15, 18, and 47)

75. Y.-M. He, G. Clark, J. R. Schaibley, Y. He, M.-C. Chen, Y.-J. Wei, X. Ding,Q. Zhang, W. Yao, X. Xu, et al., “Single quantum emitters in monolayersemiconductors,” Nat. Nanotechnol., vol. 10, no. 6, pp. 497–502, 2015.(cited on pages 13, 15, 17, 18, and 47)

76. C. Chakraborty, L. Kinnischtzke, K. M. Goodfellow, R. Beams, and A. N.Vamivakas, “Voltage-controlled quantum light from an atomically thinsemiconductor,” Nat. Nanotechnol., vol. 10, no. 6, pp. 507–511, 2015.(cited on pages 13, 15, 17, 18, and 47)

77. A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, andA. Imamoglu, “Optically active quantum dots in monolayer WSe2,” Nat.Nanotechnol., vol. 10, no. 6, pp. 491–496, 2015. (cited on pages 13, 15, 18,and 47)

78. J. L. O’brien, A. Furusawa, and J. Vuckovic, “Photonic quantum tech-nologies,” Nat. Photonics, vol. 3, no. 12, pp. 687–695, 2009. (cited onpages 13 and 18)

79. O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ul-trasensitive photodetectors based on monolayer MoS2,” Nat. Nanotech-nol., vol. 8, no. 7, pp. 497–501, 2013. (cited on pages 13, 14, and 29)

80. A. Pospischil, M. M. Furchi, and T. Mueller, “Solar-energy conversionand light emission in an atomic monolayer p-n diode,” Nat. Nanotechnol.,vol. 9, no. 4, pp. 257–261, 2014. (cited on pages 13, 14, 18, 20, and 47)

81. C.-H. Lee, G.-H. Lee, A. M. Van Der Zande, W. Chen, Y. Li, M. Han,X. Cui, G. Arefe, C. Nuckolls, T. F. Heinz, et al., “Atomically thin p–njunctions with van der waals heterointerfaces,” Nat. Nanotechnol., vol. 9,no. 9, pp. 676–681, 2014. (cited on pages 13, 14, 15, and 91)

82. M. Massicotte, P. Schmidt, F. Vialla, K. G. Schädler, A. Reserbat-Plantey,K. Watanabe, T. Taniguchi, K.-J. Tielrooij, and F. H. Koppens, “Picosec-ond photoresponse in van der Waals heterostructures,” Nat. Nanotechnol.,vol. 11, no. 1, pp. 42–46, 2016. (cited on pages 13 and 14)

83. L. Britnell, R. Ribeiro, A. Eckmann, R. Jalil, B. Belle, A. Mishchenko, Y.-J.Kim, R. Gorbachev, T. Georgiou, S. Morozov, et al., “Strong light-matterinteractions in heterostructures of atomically thin films,” Science, vol. 340,no. 6138, pp. 1311–1314, 2013. (cited on pages 13, 14, 15, and 92)

104 References

84. Z. Luo, D. Wu, B. Xu, H. Xu, Z. Cai, J. Peng, J. Weng, S. Xu, C. Zhu,F. Wang, et al., “Two-dimensional material-based saturable absorbers:towards compact visible-wavelength all-fiber pulsed lasers,” Nanoscale,vol. 8, no. 2, pp. 1066–1072, 2016. (cited on pages 14 and 15)

85. H. S. Lee, S.-W. Min, Y.-G. Chang, M. K. Park, T. Nam, H. Kim, J. H. Kim,S. Ryu, and S. Im, “MoS2 nanosheet phototransistors with thickness-modulated optical energy gap,” Nano Lett., vol. 12, no. 7, pp. 3695–3700,2012. (cited on page 13)

86. D.-S. Tsai, K.-K. Liu, D.-H. Lien, M.-L. Tsai, C.-F. Kang, C.-A. Lin, L.-J.Li, and J.-H. He, “Few-layer MoS2 with high broadband photogain andfast optical switching for use in harsh environments,” ACS Nano, vol. 7,no. 5, pp. 3905–3911, 2013. (cited on page 13)

87. J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. Mandrus,T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, et al., “Electrically tun-able excitonic light-emitting diodes based on monolayer WSe2 p-n junc-tions,” Nat. Nanotechnol., vol. 9, no. 4, pp. 268–272, 2014. (cited on pages13, 18, 20, and 47)

88. M. Fontana, T. Deppe, A. K. Boyd, M. Rinzan, A. Y. Liu, M. Paranjape,and P. Barbara, “Electron-hole transport and photovoltaic effect in gatedMoS2 schottky junctions,” Sci. Rep., vol. 3, 2013. (cited on page 13)

89. R. Sundaram, M. Engel, A. Lombardo, R. Krupke, A. Ferrari, P. Avouris,and M. Steiner, “Electroluminescence in single layer MoS2,” Nano Lett.,vol. 13, no. 4, pp. 1416–1421, 2013. (cited on pages 13 and 18)

90. R. Cheng, D. Li, H. Zhou, C. Wang, A. Yin, S. Jiang, Y. Liu, Y. Chen,Y. Huang, and X. Duan, “Electroluminescence and photocurrent gen-eration from atomically sharp WSe2/MoS2 heterojunction p–n diodes,”Nano Lett., vol. 14, no. 10, pp. 5590–5597, 2014. (cited on pages 13 and 18)

91. B. W. Baugher, H. O. Churchill, Y. Yang, and P. Jarillo-Herrero, “Opto-electronic devices based on electrically tunable p-n diodes in a monolayerdichalcogenide,” Nat. Nanotechnol., vol. 9, no. 4, pp. 262–267, 2014. (citedon pages 13, 18, and 20)

92. X. Duan, C. Wang, J. C. Shaw, R. Cheng, Y. Chen, H. Li, X. Wu, Y. Tang,Q. Zhang, A. Pan, et al., “Lateral epitaxial growth of two-dimensionallayered semiconductor heterojunctions,” Nat. Nanotechnol., vol. 9, no. 12,pp. 1024–1030, 2014. (cited on page 13)

93. F. Withers, O. Del Pozo-Zamudio, A. Mishchenko, A. Rooney,A. Gholinia, K. Watanabe, T. Taniguchi, S. Haigh, A. Geim, A. Tar-takovskii, et al., “Light-emitting diodes by band-structure engineering invan der Waals heterostructures,” Nat. Mater., vol. 14, no. 3, pp. 301–306,2015. (cited on pages 13 and 18)

References 105

94. W. J. Yu, Y. Liu, H. Zhou, A. Yin, Z. Li, Y. Huang, and X. Duan, “Highlyefficient gate-tunable photocurrent generation in vertical heterostruc-tures of layered materials,” Nat. Nanotechnol., vol. 8, no. 12, pp. 952–958,2013. (cited on pages 13 and 15)

95. H. Sun, H. Yang, L. Fang, J. Zhang, Z. Wang, and T. Jiang, “Electro-photo modulation of the fermi level in WSe2/graphene van der waalsheterojunction,” Physica E: Low-dimensional Systems and Nanostructures,vol. 88, pp. 279–283, 2017. (cited on page 13)

96. H. Yu, X. Zheng, K. Yin, and T. Jiang, “All-fiber thulium/holmium-doped mode-locked laser by tungsten disulfide saturable absorber,” LaserPhysics, vol. 27, no. 1, p. 015102, 2016. (cited on page 15)

97. K. He, C. Poole, K. F. Mak, and J. Shan, “Experimental demonstrationof continuous electronic structure tuning via strain in atomically thinMoS2,” Nano Lett., vol. 13, no. 6, pp. 2931–2936, 2013. (cited on pages 15and 16)

98. S. Mouri, Y. Miyauchi, and K. Matsuda, “Tunable photoluminescenceof monolayer MoS2 via chemical doping,” Nano Lett., vol. 13, no. 12,pp. 5944–5948, 2013. (cited on pages 15 and 16)

99. T. Korn, S. Heydrich, M. Hirmer, J. Schmutzler, and C. Schüller, “Low-temperature photocarrier dynamics in monolayer MoS2,” Appl. Phys.Lett., vol. 99, no. 10, p. 102109, 2011. (cited on pages 15 and 16)

100. Y. Chen, J. Xi, D. O. Dumcenco, Z. Liu, K. Suenaga, D. Wang, Z. Shuai,Y.-S. Huang, and L. Xie, “Tunable band gap photoluminescence fromatomically thin transition-metal dichalcogenide alloys,” ACS Nano, vol. 7,no. 5, pp. 4610–4616, 2013. (cited on pages 15 and 16)

101. H. Chen, X. Wen, J. Zhang, T. Wu, Y. Gong, X. Zhang, J. Yuan, C. Yi,J. Lou, P. M. Ajayan, et al., “Ultrafast formation of interlayer hot excitonsin atomically thin MoS2/WS2 heterostructures,” Nat. Commun., vol. 7,p. 12512, 2016. (cited on pages 15 and 91)

102. A. F. Rigosi, H. M. Hill, Y. Li, A. Chernikov, and T. F. Heinz, “Prob-ing interlayer interactions in transition metal dichalcogenide heterostruc-tures by optical spectroscopy: MoS2/WS2 and MoSe2/WSe2,” Nano Lett.,vol. 15, no. 8, pp. 5033–5038, 2015. (cited on pages 15 and 91)

103. M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel,P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, et al., “Fine structureof neutral and charged excitons in self-assembled In(Ga)As /(Al)GaAsquantum dots,” Phys. Rev. B, vol. 65, no. 19, p. 195315, 2002. (cited onpage 18)

104. G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus,C. Zhang, D. Cobden, W. Yao, and X. Xu, “Magnetic control of valleypseudospin in monolayer WSe2,” Nat. Phys., 2015. (cited on pages 18,20, 64, and 65)

106 References

105. Y.-M. He, O. Iff, N. Lundt, V. Baumann, M. Davanco, K. Srinivasan,S. Höfling, and C. Schneider, “Cascaded emission of single photons fromthe biexciton in monolayered WSe2,” Nat. Commun., vol. 7, p. 13409, 2016.(cited on pages 18 and 47)

106. T. T. Tran, S. Choi, J. A. Scott, Z.-Q. Xu, C. Zheng, G. Seniutinas, A. Ben-david, M. S. Fuhrer, M. Toth, and I. Aharonovich, “Room-temperaturesingle-photon emission from oxidized tungsten disulfide multilayers,”Adv. Opt. Mater, vol. 5, no. 5, 2017. (cited on page 18)

107. R. Hanson and D. D. Awschalom, “Coherent manipulation of singlespins in semiconductors,” Nature, vol. 453, no. 7198, pp. 1043–1049, 2008.(cited on page 18)

108. I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,”Nat. Photonics, vol. 5, no. 7, pp. 397–405, 2011. (cited on page 18)

109. Y. D. Kim, H. Kim, Y. Cho, J. H. Ryoo, C.-H. Park, P. Kim, Y. S. Kim,S. Lee, Y. Li, S.-N. Park, et al., “Bright visible light emission fromgraphene,” Nat. Nanotechnol., vol. 10, no. 8, pp. 676–681, 2015. (citedon page 18)

110. Y. Zhang, T. Oka, R. Suzuki, J. Ye, and Y. Iwasa, “Electrically switchablechiral light-emitting transistor,” Science, vol. 344, no. 6185, pp. 725–728,2014. (cited on pages 19, 20, and 63)

111. J. Xiao, Z. Ye, Y. Wang, H. Zhu, Y. Wang, and X. Zhang, “Nonlinearoptical selection rule based on valley-exciton locking in monolayer WS2,”Light. Sci. Appl., vol. 4, no. 12, p. e366, 2015. (cited on pages 19 and 20)

112. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics, vol. 8, no. 12,pp. 899–907, 2014. (cited on pages 18, 20, 22, 23, 29, 47, 48, 63, and 65)

113. H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, et al., “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotech-nol., vol. 9, no. 10, pp. 851–857, 2014. (cited on page 20)

114. K. L. Seyler, J. R. Schaibley, P. Gong, P. Rivera, A. M. Jones, S. Wu,J. Yan, D. G. Mandrus, W. Yao, and X. Xu, “Electrical control of second-harmonic generation in a WSe2 monolayer transistor,” Nat. Nanotechnol.,vol. 10, no. 5, pp. 407–411, 2015. (cited on pages 20, 21, 22, 75, and 87)

115. Z. Wang, J. Shan, and K. F. Mak, “Valley-and spin-polarized Landaulevels in monolayer WSe2,” Nat. Nanotechnol., 2016. (cited on pages 20and 64)

116. H. Rostami and R. Asgari, “Valley zeeman effect and spin-valley polar-ized conductance in monolayer MoS2 in a perpendicular magnetic field,”Phys. Rev. B, vol. 91, no. 7, p. 075433, 2015. (cited on pages 20 and 64)

References 107

117. A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, andA. Imamoglu, “Valley zeeman effect in elementary optical excitationsof monolayer WSe2,” Nat. Phys., 2015. (cited on pages 20 and 64)

118. Y. Li, J. Ludwig, T. Low, A. Chernikov, X. Cui, G. Arefe, Y. D. Kim,A. M. van der Zande, A. Rigosi, H. M. Hill, S. H. Kim, J. Hone, Z. Li,D. Smirnov, and T. F. Heinz, “Valley splitting and polarization by theZeeman effect in monolayer MoSe2,” Phys. Rev. Lett., vol. 113, p. 266804,Dec 2014. (cited on pages 20 and 64)

119. A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker,“Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2and MoS2 to 65 Tesla,” Nat. Commun., vol. 7, 2016. (cited on pages 20and 64)

120. Z. Ye, D. Sun, and T. F. Heinz, “Optical manipulation of valley pseu-dospin,” Nat. Phys., 2016. (cited on pages 20, 64, and 65)

121. W.-T. Hsu, Y.-L. Chen, C.-H. Chen, P.-S. Liu, T.-H. Hou, L.-J. Li, and W.-H.Chang, “Optically initialized robust valley-polarized holes in monolayerWSe2,” Nat. Commun., vol. 6, pp. 8963–8963, 2014. (cited on pages 20and 64)

122. T. Smolenski, M. Goryca, M. Koperski, C. Faugeras, T. Kazimierczuk,A. Bogucki, K. Nogajewski, P. Kossacki, and M. Potemski, “Tuning valleypolarization in a WSe2 monolayer with a tiny magnetic field,” Phys. Rev.X, vol. 6, no. 2, p. 021024, 2016. (cited on pages 20, 64, and 65)

123. R. Boyd, Nonlinear Optics. Nonlinear Optics Series, London: AcademicPress, 2008. (cited on pages 20 and 22)

124. L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M.de Paula, “Observation of intense second harmonic generation fromMoS2 atomic crystals,” Phys. Rev. B, vol. 87, no. 20, p. 201401, 2013. (citedon pages 20, 22, 47, 75, and 81)

125. N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, andH. Zhao, “Second harmonic microscopy of monolayer MoS2,” Phys. Rev.B, vol. 87, no. 16, p. 161403, 2013. (cited on pages 20, 21, 22, 75, and 81)

126. X. Zheng, Y. Zhang, R. Chen, Z. Xu, and T. Jiang, “Z-scan measurementof the nonlinear refractive index of monolayer WS2,” Opt. Express, vol. 23,no. 12, pp. 15616–15623, 2015. (cited on page 20)

127. D. Li, W. Xiong, L. Jiang, Z. Xiao, H. Rabiee Golgir, M. Wang, X. Huang,Y. Zhou, Z. Lin, J. Song, et al., “Multimodal nonlinear optical imagingof MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano,vol. 10, no. 3, pp. 3766–3775, 2016. (cited on page 20)

128. R. Wang, H.-C. Chien, J. Kumar, N. Kumar, H.-Y. Chiu, and H. Zhao,“Third-harmonic generation in ultrathin films of MoS2,” ACS Appl.Mater. Interfaces, vol. 6, no. 1, pp. 314–318, 2013. (cited on page 20)

108 References

129. C. Torres-Torres, N. Perea-López, A. L. Elías, H. R. Gutiérrez, D. A.Cullen, A. Berkdemir, F. López-Urías, H. Terrones, and M. Terrones,“Third order nonlinear optical response exhibited by mono-and few-layers of WS2,” 2D Mater., vol. 3, no. 2, p. 021005, 2016. (cited on page20)

130. H. Zhao, Q. Guo, F. Xia, and H. Wang, “Two-dimensional materials fornanophotonics application,” Nanophotonics, vol. 4, no. 1, pp. 128–142,2015. (cited on pages 20 and 22)

131. D. J. Lockwood and L. Pavesi, Silicon photonics. New York: Springer-verlag, 2004. (cited on pages 20, 22, 49, and 78)

132. X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O. Brien, J. C. Hone, and X. Zhang,“Edge nonlinear optics on a MoS2 atomic monolayer,” Science, vol. 344,no. May, pp. 488–491, 2014. (cited on pages 21, 22, 75, and 81)

133. E. Mishina, N. Sherstyuk, S. Lavrov, A. Sigov, A. Mitioglu, S. Anghel,and L. Kulyuk, “Observation of two polytypes of MoS2 ultrathin layersstudied by second harmonic generation microscopy and photolumines-cence,” Appl. Phys. Lett., vol. 106, no. 13, p. 131901, 2015. (cited on pages21, 22, 75, and 81)

134. Y. Li, Y. Rao, K. F. Mak, Y. You, S. Wang, C. R. Dean, and T. F. Heinz,“Probing symmetry properties of few-layer MoS2 and h-BN by opticalsecond-harmonic generation,” Nano Lett., vol. 13, no. 7, pp. 3329–3333,2013. (cited on pages 22, 47, 75, and 81)

135. C. T. Le, D. J. Clark, F. Ullah, V. Senthilkumar, J. I. Jang, Y. Sim, M.-J.Seong, K.-H. Chung, H. Park, and Y. S. Kim, “Nonlinear optical char-acteristics of monolayer MoSe2,” Ann. Phys. (Berlin), vol. 528, no. 7-8,pp. 551–559, 2016. (cited on pages 22 and 75)

136. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Ter-rones, V. Crespi, and Z. Liu, “Extraordinary second harmonic generationin tungsten disulfide monolayers,” Sci. Rep., vol. 4, p. 5530, 2014. (citedon pages 22, 47, and 75)

137. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L.Brongersma, “Plasmonics for extreme light concentration and manipu-lation,” Nat. Mater., vol. 9, no. 3, pp. 193–204, 2010. (cited on pages 22and 29)

138. L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photonics, vol. 5,no. 2, pp. 83–90, 2011. (cited on page 22)

139. A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express, vol. 20, no. 18, pp. 20599–20604, 2012. (cited on page 22)

140. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by pho-tonic crystals and nanocavities,” Nature photonics, vol. 1, no. 8, pp. 449–458, 2007. (cited on pages 22 and 24)

References 109

141. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,”Phys. Rev., vol. 69, pp. 37–38, 1946. (cited on pages 23, 29, and 32)

142. E. Merzbacher, Quantum Mechanics 3rd edn. Wiley, 1997. (cited on page23)

143. Modern Quantum Mechanics. Addison-Wesley, revised edition ed., 1994.(cited on page 23)

144. M. Pelton, “Modified spontaneous emission in nanophotonic structures,”Nat. Photonics, vol. 9, no. 7, pp. 427–435, 2015. (cited on pages 23 and 44)

145. N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmonsin strongly coupled metallic nanostructures,” Chem. Rev, vol. 111, no. 6,pp. 3913–3961, 2011. (cited on page 24)

146. J. B. Khurgin, “How to deal with the loss in plasmonics and metamate-rials,” Nature nanotechnology, vol. 10, no. 1, pp. 2–6, 2015. (cited on page24)

147. S. Wu, S. Buckley, J. R. Schaibley, L. Feng, J. Yan, D. G. Mandrus,F. Hatami, W. Yao, J. Vuckovic, and A. Majumdar, “Monolayer semi-conductor nanocavity lasers with ultralow thresholds,” Nature, vol. 520,no. 7545, pp. 69–72, 2015. (cited on pages 25, 26, and 47)

148. X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, andV. M. Menon, “Strong light–matter coupling in two-dimensional atomiccrystals,” Nat. Photonics, vol. 9, no. 1, pp. 30–34, 2015. (cited on pages 25and 26)

149. X. Gan, Y. Gao, K. Fai Mak, X. Yao, R.-J. Shiue, A. van der Zande, M. E.Trusheim, F. Hatami, T. F. Heinz, J. Hone, et al., “Controlling the spon-taneous emission rate of monolayer MoS2 in a photonic crystal nanocav-ity,” Appl. Phys. Lett., vol. 103, no. 18, p. 181119, 2013. (cited on pages 25and 26)

150. S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G.Mandrus, W. Yao, F. Hatami, J. Vuckovic, M. Arka, and X. Xiaodong,“Control of two-dimensional excitonic light emission via photonic crys-tal,” 2D Mater., vol. 1, no. 1, p. 011001, 2014. (cited on pages 26 and 48)

151. S. Dufferwiel, S. Schwarz, F. Withers, A. Trichet, F. Li, M. Sich, C. Clark,A. Nalitov, D. Solnyshkov, G. Malpuech, K. Novoselov, J. Smith, M. Skol-nick, D. Krizhanovskii, and A. Tartakovskii, “Exciton-polaritons in vander Waals heterostructures embedded in tunable microcavities.,” Nat.Commun., vol. 6, pp. 8579–8579, 2014. (cited on page 26)

152. Y. Ye, Z. J. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang,“Monolayer excitonic laser,” Nat. Photonics, vol. 9, pp. 733–737, 2015.(cited on pages 26 and 47)

110 References

153. S. Wu, S. Buckley, J. R. Schaibley, L. Feng, J. Yan, D. G. Mandrus,F. Hatami, W. Yao, J. Vuckovic, A. Majumdar, and X. Xu, “Mono-layer semiconductor nanocavity lasers with ultralow thresholds,” Nature,vol. 520, no. 7545, pp. 69–72, 2015. (cited on page 29)

154. J. Lin, H. Li, H. Zhang, and W. Chen, “Plasmonic enhancement of pho-tocurrent in MoS2 field-effect-transistor,” Appl. Phys. Lett., vol. 102, no. 20,p. 203109, 2013. (cited on pages 29 and 30)

155. S. Najmaei, A. Mlayah, A. Arbouet, C. Girard, J. Léotin, and J. Lou, “Plas-monic pumping of excitonic photoluminescence in hybrid MoS2 −Aunanostructures,” ACS Nano, vol. 8, no. 12, pp. 12682–12689, 2014. (citedon pages 29, 30, 38, and 48)

156. A. Sobhani, A. Lauchner, S. Najmaei, C. Ayala-Orozco, F. Wen, J. Lou,and N. J. Halas, “Enhancing the photocurrent and photoluminescenceof single crystal monolayer MoS2 with resonant plasmonic nanoshells,”Appl. Phys. Lett., vol. 104, no. 3, p. 031112, 2014. (cited on pages 29, 30,and 48)

157. G. M. Akselrod, T. Ming, C. Argyropoulos, T. B. Hoang, Y. Lin, X. Ling,D. R. Smith, J. Kong, and M. H. Mikkelsen, “Leveraging nanocavity har-monics for control of optical processes in 2D semiconductors,” Nano Lett.,vol. 15, no. 5, pp. 3578–3584, 2015. (cited on pages 29, 30, and 48)

158. B. Lee, J. Park, G. H. Han, H.-S. Ee, C. H. Naylor, W. Liu, A. C. John-son, and R. Agarwal, “Fano resonance and spectrally modified photolu-minescence enhancement in monolayer MoS2 integrated with plasmonicnanoantenna array,” Nano Lett., vol. 15, no. 5, pp. 3646–3653, 2015. (citedon pages 30 and 31)

159. U. Bhanu, M. R. Islam, L. Tetard, and S. I. Khondaker, “Photolumi-nescence quenching in gold-MoS2 hybrid nanoflakes,” Sci. Rep., vol. 4,p. 5575, 2014. (cited on pages 30, 31, and 38)

160. S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett.,vol. 15, no. 4, pp. 2700–2704, 2015. (cited on pages 29, 38, and 48)

161. D. O. Sigle, J. Mertens, L. O. Herrmann, R. W. Bowman, B. Dubertret,Y. Shi, H. Y. Yang, C. Tserkezis, J. Aizpurua, and J. J. Baumberg, “Mon-itoring morphological changes in 2D monolayer semiconductors usingatom-thick plasmonic nanocavities,” ACS Nano, vol. 9, pp. 825–830, 2015.(cited on page 31)

162. K. M. Goodfellow, R. Beams, C. Chakraborty, L. Novotny, and A. N.Vamivakas, “Integrated nanophotonics based on nanowire plasmons andatomically thin material,” Optica, vol. 1, no. 3, pp. 149–152, 2014. (citedon page 31)

References 111

163. J. Kern, A. Trügler, I. Niehues, J. Ewering, R. Schmidt, R. Schneider,S. Najmaei, A. George, J. Zhang, J. Lou, U. Hohenester, S. M. de Vascon-cellos, and R. Bratschitsch, “Nanoantenna-enhanced light-matter interac-tion in atomically thin WS2,” ACS Photonics, vol. 2, no. 9, pp. 1260–1265,2015. (cited on page 31)

164. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching ofsingle-molecule fluorescence,” Phys. Rev. Lett., vol. 96, no. 11, p. 113002,2006. (cited on pages 31, 32, 38, 41, 49, and 65)

165. S. Tongay, J. Zhou, C. Ataca, K. Lo, T. S. Matthews, J. Li, J. C. Gross-man, and J. Wu, “Thermally driven crossover from indirect toward directbandgap in 2D semiconductors: MoSe2 versus MoS2,” Nano Lett., vol. 12,no. 11, pp. 5576–5580, 2012. (cited on pages 31, 36, and 75)

166. N. Kumar, Q. Cui, F. Ceballos, D. He, Y. Wang, and H. Zhao,“Exciton-exciton annihilation in MoSe2 monolayers,” Phys. Rev. B, vol. 89,p. 125427, 2014. (cited on page 31)

167. C. Zhang, A. Johnson, C.-L. Hsu, L.-J. Li, and C.-K. Shih, “Direct imagingof band profile in single layer MoS2 on graphite: quasiparticle energygap, metallic edge states, and edge band bending,” Nano Lett., vol. 14,no. 5, pp. 2443–2447, 2014. (cited on pages 31 and 79)

168. J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and het-erostructures of two-dimensional semiconductors,” Appl. Phys. Lett.,vol. 102, no. 1, p. 012111, 2013. (cited on pages 31 and 38)

169. M. Thomas, J.-J. Greffet, R. Carminati, and J. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,”Appl. Phys. Lett., vol. 85, no. 17, pp. 3863–3865, 2004. (cited on page32)

170. R. Carminati, J.-J. Greffet, C. Henkel, and J. Vigoureux, “Radiative andnon-radiative decay of a single molecule close to a metallic nanoparticle,”Opt. Commun., vol. 261, no. 2, pp. 368–375, 2006. (cited on page 32)

171. H. Mertens, A. Koenderink, and A. Polman, “Plasmon-enhanced lumi-nescence near noble-metal nanospheres: comparison of exact theory andan improved Gersten and Nitzan model,” Phys. Rev. B, vol. 76, no. 11,p. 115123, 2007. (cited on page 32)

172. A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficientoptical nanoantenna,” Phys. Rev. B, vol. 78, p. 195111, Nov 2008. (citedon page 32)

173. G. Colas des Francs, A. Bouhelier, E. Finot, J.-C. Weeber, A. Dereux,C. Girard, and E. Dujardin, “Fluorescence relaxation in the near–field ofa mesoscopic metallic particle: distance dependence and role of plasmonmodes,” Opt. Express, vol. 16, no. 22, pp. 17654–17666, 2008. (cited onpage 32)

112 References

174. A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric opti-cal antenna for ultra directional and enhanced radiative emission,” ACSNano, vol. 4, no. 6, pp. 3390–3396, 2010. (cited on page 32)

175. J.-W. Liaw, C.-S. Chen, and J.-H. Chen, “Enhancement or quenching ef-fect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc.Radiat. Transfer, vol. 111, no. 3, pp. 454–465, 2010. (cited on page 32)

176. P. Tonndorf, R. Schmidt, P. Böttger, X. Zhang, J. Börner, A. Liebig,M. Albrecht, C. Kloc, O. Gordan, D. R. T. Zahn, S. M. D. Vasconcel-los, and R. Bratschitsch, “Photoluminescence emission and Raman re-sponse of monolayer MoS2, MoSe2, and WSe2,” Opt. Express, vol. 21,no. 4, pp. 4908–4916, 2013. (cited on pages 36 and 79)

177. P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,”Phys. Rev. B, vol. 6, no. 12, p. 4370, 1972. (cited on pages 40 and 69)

178. S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki,“Room-temperature deposition of indium tin oxide thin films withplasma ion-assisted evaporation,” Thin Solid Films, vol. 335, no. 1, pp. 1–5, 1998. (cited on page 40)

179. J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan,and R. Zia, “Orientation of luminescent excitons in layered nanomateri-als,” Nat. Nanotechnol., vol. 8, no. 4, pp. 271–276, 2013. (cited on pages41, 55, 57, and 67)

180. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt.Photonics, vol. 1, no. 3, pp. 438–483, 2009. (cited on page 41)

181. J. S. Ponraj, Z.-Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li,S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, andQ. Bao, “Photonics and optoelectronics of two-dimensional materials be-yond graphene,” Nanotechnology, vol. 27, no. 46, p. 462001, 2016. (citedon page 47)

182. O. Salehzadeh, M. Djavid, N. H. Tran, I. Shih, and Z. Mi, “Opticallypumped two-dimensional MoS2 lasers operating at room-temperature,”Nano Lett., vol. 15, no. 8, pp. 5302–5306, 2015. (cited on page 47)

183. T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantumemission from hexagonal boron nitride monolayers,” Nat. Nanotechnol.,vol. 11, no. 1, pp. 37–41, 2016. (cited on pages 47 and 91)

184. M. Weismann and N. C. Panoiu, “Theoretical and computational anal-ysis of second-and third-harmonic generation in periodically patternedgraphene and transition-metal dichalcogenide monolayers,” Phys. Rev. B,vol. 94, no. 3, p. 035435, 2016. (cited on pages 47, 81, and 92)

185. H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti,D. de Ceglia, C. De Angelis, Y. Lu, and D. N. Neshev, “Enhanced secondharmonic generation from two-dimensional MoSe2 on a silicon waveg-uide,” Light. Sci. Appl., vol. 6, p. e17060, 2017. (cited on pages 47 and 49)

References 113

186. D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light meta-surfaces based on single-crystal silicon,” ACS Photonics, vol. 3, no. 10,pp. 1919–1925, 2016. (cited on page 47)

187. I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophoton-ics,” Nat. Photonics, vol. 11, no. 5, pp. 274–284, 2017. (cited on pages 47and 91)

188. D. Liang, G. Roelkens, R. Baets, and J. E. Bowers, “Hybrid integratedplatforms for silicon photonics,” Materials, vol. 3, no. 3, pp. 1782–1802,2010. (cited on pages 47 and 76)

189. N. Youngblood and L. Mo, “Integration of 2D materials on a sili-con photonics platform for optoelectronics applications,” Nanophotonics,vol. https://doi.org/10.1515/nanoph-2016-0155, 2016. (cited on page47)

190. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layeredmaterials,” Nat. Photonics, vol. 10, no. 4, pp. 227–238, 2016. (cited onpage 47)

191. Y. J. Noori, Y. Cao, J. Roberts, C. Woodhead, R. Bernardo-Gavito, P. Tovee,and R. J. Young, “Photonic crystals for enhanced light extraction from 2Dmaterials,” ACS Photonics, vol. 3, no. 12, pp. 2515–2520, 2016. (cited onpages 48 and 67)

192. D.-H. Lien, J. S. Kang, M. Amani, K. Chen, M. Tosun, H.-P. Wang, T. Roy,M. S. Eggleston, M. C. Wu, and M. Dubey, “Engineering light outcou-pling in 2D materials,” Nano Lett., vol. 15, no. 2, pp. 1356–1361, 2015.(cited on page 48)

193. H. Chen, J. Yang, E. Rusak, J. Straubel, R. Guo, Y. W. Myint, J. Pei,M. Decker, I. Staude, C. Rockstuhl, et al., “Manipulation of photolumi-nescence of two-dimensional MoSe2 by gold nanoantennas,” Scientificreports, vol. 6, 2016. (cited on pages 48 and 79)

194. Z. Wang, Z. Dong, Y. Gu, Y.-H. Chang, L. Zhang, L.-J. Li, W. Zhao,G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. W. Yan, C.-W. Qiu,and A. T. S. Wee, “Giant photoluminescence enhancement in tungsten-diselenide–gold plasmonic hybrid structures,” Nat. Commun., vol. 7,p. 11283, 2016. (cited on page 48)

195. T. Galfsky, Z. Sun, C. R. Considine, C.-T. Chou, W.-C. Ko, Y.-H. Lee, E. E.Narimanov, and V. M. Menon, “Broadband enhancement of spontaneousemission in two-dimensional semiconductors using photonic hypercrys-tals,” Nano Lett., vol. 16, no. 8, pp. 4940–4945, 2016. (cited on page 48)

196. X. Gai, D.-Y. Choi, and B. Luther-Davies, “Negligible nonlinear absorp-tion in hydrogenated amorphous silicon at 1.55 µm for ultra-fast nonlin-ear signal processing,” Opt. Express, vol. 22, no. 8, pp. 9948–9958, 2014.(cited on pages 51 and 78)

114 References

197. T. Yan, X. Qiao, X. Liu, P. Tan, and X. Zhang, “Photoluminescence proper-ties and exciton dynamics in monolayer WSe2,” Appl. Phys. Lett., vol. 105,no. 10, p. 101901, 2014. (cited on page 54)

198. J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finiteelement method for simulation of optical nano structures,” Phys. StatusSolidi B, vol. 244, no. 10, pp. 3419–3434, 2007. (cited on page 54)

199. L. Zschiedrich, H. J. Greiner, S. Burger, and F. Schmidt, “Numerical anal-ysis of nanostructures for enhanced light extraction from OLEDS,” inSPIE OPTO, pp. 86410B–86410B, International Society for Optics andPhotonics, 2013. (cited on page 57)

200. W. Yao, D. Xiao, and Q. Niu, “Valley-dependent optoelectronics frominversion symmetry breaking,” Phys. Rev. B, vol. 77, no. 23, p. 235406,2008. (cited on page 63)

201. A. Rycerz, J. Tworzydło, and C. Beenakker, “Valley filter and valley valvein graphene,” Nat. Phys., vol. 3, no. 3, pp. 172–175, 2007. (cited on page63)

202. D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene:magnetic moment and topological transport,” Phys. Rev. Lett., vol. 99,no. 23, p. 236809, 2007. (cited on page 63)

203. Y. Shkolnikov, E. De Poortere, E. Tutuc, and M. Shayegan, “Valley split-ting of AlAs two-dimensional electrons in a perpendicular magneticfield,” Phys. Rev. Lett., vol. 89, no. 22, p. 226805, 2002. (cited on page63)

204. S. Wolf, D. Awschalom, R. Buhrman, J. Daughton, S. Von Molnar,M. Roukes, A. Y. Chtchelkanova, and D. Treger, “Spintronics: a spin-based electronics vision for the future,” Science, vol. 294, no. 5546,pp. 1488–1495, 2001. (cited on page 63)

205. F. J. Ohkawa and Y. Uemura, “Theory of valley splitting in an N-channel(100) inversion layer of Si III : enhancement of splittings by many-bodyeffects,” J. Phys. Soc. Jpn., vol. 43, no. 3, pp. 925–932, 1977. (cited on page63)

206. S. Wu, J. S. Ross, G.-B. Liu, G. Aivazian, A. Jones, Z. Fei, W. Zhu, D. Xiao,W. Yao, D. Cobden, et al., “Electrical tuning of valley magnetic momentthrough symmetry control in bilayer MoS2,” Nat. Phys., vol. 9, no. 3,pp. 149–153, 2013. (cited on pages 64 and 65)

207. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancementof single-molecule fluorescence using a gold nanoparticle as an opticalnanoantenna,” Phys. Rev. Lett., vol. 97, no. 1, p. 017402, 2006. (cited onpage 65)

208. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger,T. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent

References 115

molecules with single plasmonic nanoresonators,” Phys. Rev. Lett.,vol. 100, no. 20, p. 203002, 2008. (cited on page 65)

209. M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, et al., “Exci-tation of dark plasmons in metal nanoparticles by a localized emitter,”Phys. Rev. Lett., vol. 102, no. 10, p. 107401, 2009. (cited on page 66)

210. A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant,and N. F. Van Hulst, “Multipolar radiation of quantum emitters withnanowire optical antennas,” Nat. Commun., vol. 4, p. 1750, 2013. (citedon pages 66 and 73)

211. S. Rodriguez, F. B. Arango, T. Steinbusch, M. Verschuuren, A. Koen-derink, and J. G. Rivas, “Breaking the symmetry of forward-backwardlight emission with localized and collective magnetoelectric resonancesin arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett.,vol. 113, no. 24, p. 247401, 2014. (cited on page 66)

212. S. S. Kruk, M. Decker, I. Staude, S. Schlecht, M. Greppmair, D. N. Ne-shev, and Y. S. Kivshar, “Spin-polarized photon emission by resonantmultipolar nanoantennas,” ACS Photonics, vol. 1, no. 11, pp. 1218–1223,2014. (cited on page 66)

213. A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole lightscattering by nonspherical nanoparticles in the discrete dipole approx-imation,” Phys. Rev. B, vol. 84, p. 235429, 2011. (cited on page 66)

214. I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. vanHulst, “Multipolar interference for directed light emission,” Nano Lett.,vol. 14, no. 1, pp. 166–171, 2013. (cited on pages 67 and 73)

215. J. D. Jackson, Classical Electrodynamics. New York: John Wiley & Sons,1998. (cited on page 67)

216. C. D. Abernethy, G. M. Codd, M. D. Spicer, and M. K. Taylor, “A highlystable N-heterocyclic carbene complex of trichloro-oxo-vanadium(v) dis-playing novel Cl—C(carbene) bonding interactions,” J. Am. Chem. Soc.,vol. 125, no. 5, pp. 1128–1129, 2003. (cited on page 67)

217. J. N. Coleman, M. Lotya, A. O,Neill, S. D. Bergin, P. J. King, U. Khan,K. Young, A. Gaucher, S. De, R. J. Smith, et al., “Two-dimensionalnanosheets produced by liquid exfoliation of layered materials,” Science,vol. 331, no. 6017, pp. 568–571, 2011. (cited on page 72)

218. J. Choi, H. Chen, F. Li, L. Yang, S. S. Kim, R. R. Naik, P. D. Ye, andJ. H. Choi, “Nanomanufacturing of 2D transition metal dichalcogenidematerials using self-assembled DNA nanotubes,” Small, vol. 11, no. 41,pp. 5520–5527, 2015. (cited on page 72)

219. F. Cheng, H. Xu, W. Xu, P. Zhou, J. Martin, and K. P. Loh, “Controlledgrowth of 1D MoSe2 nanoribbons with spatially modulated edge states,”Nano Lett., vol. 17, no. 2, pp. 1116–1120, 2017. (cited on page 72)

116 References

220. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. Mo-erner, “Large single-molecule fluorescence enhancements produced by abowtie nanoantenna,” Nat. Photonics, vol. 3, no. 11, pp. 654–657, 2009.(cited on page 73)

221. I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photonemitters,” Nat. Photonics, vol. 10, no. 10, pp. 631–641, 2016. (cited onpage 75)

222. H. Zeng, G.-b. Liu, J. Dai, Y. Yan, B. Zhu, R. He, L. Xie, and S. Xu,“Optical signature of symmetry variations and spin-valley coupling inatomically thin tungsten dichalcogenides,” Sci. Rep., vol. 3, 2013. (citedon page 75)

223. F. Yi, M. Ren, J. C. Reed, H. Zhu, J. Hou, C. H. Naylor, A. C. Johnson,R. Agarwal, and E. Cubukcu, “Optomechanical enhancement of doublyresonant 2D optical nonlinearity,” Nano letters, vol. 16, no. 3, pp. 1631–1636, 2016. (cited on pages 75 and 76)

224. A. M. Jones, H. Yu, J. R. Schaibley, J. Yan, D. G. Mandrus, T. Taniguchi,K. Watanabe, H. Dery, W. Yao, and X. Xu, “Excitonic luminescence up-conversion in a two-dimensional semiconductor,” Nat. Phys., vol. 12,no. April, pp. 8–13, 2016. (cited on page 75)

225. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Ter-rones, V. Crespi, and Z. Liu, “Extraordinary second harmonic generationin tungsten disulfide monolayers,” Scientific reports, vol. 4, p. 5530, 2014.(cited on pages 75 and 84)

226. M. L. Trolle, Y.-C. Tsao, K. Pedersen, and T. G. Pedersen, “Observation ofexcitonic resonances in the second harmonic spectrum of MoS2,” PhysicalReview B, vol. 92, no. 16, p. 161409, 2015. (cited on page 75)

227. J. Zeng, M. Yuan, W. Yuan, Q. Dai, H. Fan, S. Lan, and S. Tie, “En-hanced second harmonic generation of MoS2 layers on a thin gold film,”Nanoscale, vol. 7, no. 32, pp. 13547–13553, 2015. (cited on pages 75and 76)

228. J. K. Day, M.-H. Chung, Y.-H. Lee, and V. M. Menon, “Microcavity en-hanced second harmonic generation in 2D MoS2,” Opt. Mater. Express,vol. 6, no. 7, pp. 2360–2365, 2016. (cited on pages 75 and 76)

229. T. K. Fryett, K. L. Seyler, J. Zheng, C.-H. Liu, X. Xu, and A. Majumdar,“Silicon photonic crystal cavity enhanced second-harmonic generationfrom monolayer WSe2,” 2D Mater., vol. 4, no. 1, p. 015031, 2016. (citedon pages 75 and 76)

230. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat.Photonics, vol. 4, no. 8, pp. 535–544, 2010. (cited on page 76)

231. M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. De-goli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pier-obon, and L. Pavesi, “Second harmonic generation in silicon waveguides

References 117

strained by silicon nitride,” Nat. Mater., vol. 11, no. 2, pp. 148–154, 2012.(cited on page 76)

232. A. S. Solntsev and A. A. Sukhorukov, “Combined frequency conver-sion and pulse compression in nonlinear tapered waveguides,” Opt. Lett.,vol. 37, pp. 446–448, Feb 2012. (cited on page 76)

233. M. Arka, M. D. Christopher, K. F. Taylor, Z. Alan, B. Sonia, and G. Dario,“Hybrid 2D material nanophotonics: A scalable platform for low-powernonlinear and quantum optics,” ACS Photonics, vol. 2, no. 8, pp. 1160–1166, 2015. (cited on page 76)

234. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne,S. Wang, J. Lapointe, R. Halir, A. O.-M. nux, S. Janz, and M. Dado,“Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Ex-press, vol. 23, pp. 22628–22635, Aug 2015. (cited on page 78)

235. D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson,M. Nedeljkovic, X. Chen, D. Van Thourhout, S. Keyvaninia, and S. K. Sel-varaja, “Silicon photonic integration platform?have we found the sweetspot?,” IEEE J. Sel. Top. Quantum, vol. 20, no. 4, pp. 189–205, 2014. (citedon page 78)

236. D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil,D. V. Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grat-ing couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express, vol. 18, pp. 18278–18283, Aug 2010.(cited on page 78)

237. S. A. Masturzo, J. M. Yarrison-Rice, H. E. Jackson, and J. T. Boyd, “Grat-ing couplers fabricated by electron-beam lithography for coupling free-space light into nanophotonic devices,” IEEE Trans. Nanotechnol., vol. 6,pp. 622–626, Nov 2007. (cited on page 78)

238. C. R. Doerr and L. L. Buhl, “Circular grating coupler for creating focusedazimuthally and radially polarized beams,” Opt. Lett., vol. 36, no. 7,pp. 1209–1211, 2011. (cited on page 78)

239. H. A. Haus and G. A. Reider, “Enhancement of surface second harmonicgeneration with waveguides,” Appl. Opt., vol. 26, pp. 4576–4580, Nov1987. (cited on page 81)

240. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quant.Electron., vol. 9, pp. 919–933, 1973. (cited on page 83)

241. M. N. Ali, J. Xiong, S. Flynn, J. Tao, Q. D. Gibson, L. M. Schoop,T. Liang, N. Haldolaarachchige, M. Hirschberger, N. Ong, et al., “Large,non-saturating magnetoresistance in WTe2,” Nature, vol. 514, no. 7521,pp. 205–208, 2014. (cited on page 91)

118 References

242. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and D. Y. Peide,“Phosphorene: an unexplored 2D semiconductor with a high hole mo-bility,” ACS Nano, 2014. (cited on page 91)

243. P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C.Asensio, A. Resta, B. Ealet, and G. Le Lay, “Silicene: compelling exper-imental evidence for graphenelike two-dimensional silicon,” Phys. Rev.Lett., vol. 108, no. 15, p. 155501, 2012. (cited on page 91)

244. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar,and B. Luk,yanchuk, “Optically resonant dielectric nanostructures,” Sci-ence, vol. 354, no. 6314, p. aag2472, 2016. (cited on page 91)

245. J. M. Hamm and O. Hess, “Two two-dimensional materials are betterthan one,” Science, vol. 340, no. 6138, pp. 1298–1299, 2013. (cited onpage 92)

246. K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D ma-terials and van der Waals heterostructures,” Science, vol. 353, no. 6298,p. aac9439, 2016. (cited on page 92)

247. Y. N. Gartstein, X. Li, and C. Zhang, “Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer,”Phys. Rev. B, vol. 92, no. 7, p. 075445, 2015. (cited on page 92)

248. L. Sun, Q. Wang, B. Zhang, X. Shen, and W. Lu, “Room temperatureexciton polaritons in thin WS2 flakes,” in Frontiers in Optics, pp. FF5H–2,Optical Society of America, 2016. (cited on page 92)

249. F. Hu, Y. Luan, M. Scott, J. Yan, D. Mandrus, X. Xu, and Z. Fei, “Imagingexciton–polariton transport in MoSe2 waveguides,” Nat. Photonics, 2017.(cited on page 92)

250. M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler,and A. Imamoglu, “Fermi polaron-polaritons in charge-tunable atomi-cally thin semiconductors,” Nat. Phys., vol. 13, no. 3, pp. 255–261, 2017.(cited on page 92)

251. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C.Saraswat, and D. A. Miller, “Nanometre-scale germanium photodetectorenhanced by a near-infrared dipole antenna,” Nat. Photonics, vol. 2, no. 4,pp. 226–229, 2008. (cited on page 92)

252. C.-C. Chang, Y. D. Sharma, Y.-S. Kim, J. A. Bur, R. V. Shenoi, S. Kr-ishna, D. Huang, and S.-Y. Lin, “A surface plasmon enhanced infraredphotodetector based on InAs quantum dots,” Nano Lett., vol. 10, no. 5,pp. 1704–1709, 2010. (cited on page 92)

253. Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, andX. Duan, “Plasmon resonance enhanced multicolour photodetection bygraphene,” Nat. Commun., vol. 2, p. 579, 2011. (cited on page 92)

References 119

254. M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz,P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, et al., “Microcavity-integrated graphene photodetector,” Nano Lett., vol. 12, no. 6, pp. 2773–2777, 2012. (cited on page 92)

255. P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera,S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, et al., “Con-trolling graphene plasmons with resonant metal antennas and spatialconductivity patterns,” Science, vol. 344, no. 6190, pp. 1369–1373, 2014.(cited on page 92)

256. T. T. Tran, D. Wang, Z.-Q. Xu, A. Yang, M. Toth, T. W. Odom, andI. Aharonovich, “Deterministic coupling of quantum emitters in 2Dmaterials to plasmonic nanocavity arrays,” Nano Lett., vol. 17, no. 4,pp. 2634–2639, 2017. (cited on page 92)

257. A. Branny, S. Kumar, R. Proux, and B. D. Gerardot, “Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconduc-tor,” Nat. Commun., vol. 8, 2017. (cited on page 92)

258. F. Liu, S. Song, D. Xue, and H. Zhang, “Folded structured graphenepaper for high performance electrode materials,” Adv. Mater., vol. 24,no. 8, pp. 1089–1094, 2012. (cited on page 92)

manipulation of light-emitting properties of 2d materials by photonic nanostructures

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